Subthreshold Regime Research Articles

Linked Gauss-Diffusion processes for modeling a finite-size neuronal network

A Leaky Integrate-and-Fire (LIF) model with stochastic current-based linkages is considered to describe the firing activity of neurons interacting in a (2×2)-size feed-forward network. In the subthreshold regime and under the assumption that no more than one spike is exchanged between coupled neurons, the stochastic evolution of the neuronal membrane voltage is subject to random jumps due to interactions in the network. Linked Gauss-Diffusion processes are proposed to describe this dynamics and to provide estimates of the firing probability density of each neuron. To this end, an iterated integral equation-based approach is applied to evaluate numerically the first passage time density of such processes through the firing threshold. Asymptotic approximations of the firing densities of surrounding neurons are used to obtain closed-form expressions for the mean of the involved processes and to simplify the numerical procedure. An extension of the model to an (N×N)-size network is also given. Histograms of firing times obtained by simulations of the LIF dynamics and numerical firings estimates are compared.

Accurate analytical modeling of junctionless DG-MOSFET by green's function approach

An accurate analytical model of Junctionless double gate MOSFET (JL-DG-MOSFET) in the subthreshold regime of operation is developed in this work using green's function approach. The approach considers 2-D mixed boundary conditions and multi-zone techniques to provide an exact analytical solution to 2-D Poisson's equation. The Fourier coefficients are calculated correctly to derive the potential equations that are further used to model the channel current and subthreshold slope of the device. The threshold voltage roll-off is computed from parallel shifts of Ids-Vgs curves between the long channel and short-channel devices. It is observed that the green's function approach of solving 2-D Poisson's equation in both oxide and silicon region can accurately predict channel potential, subthreshold current (Isub), threshold voltage (Vt) roll-off and subthreshold slope (SS) of both long & short channel devices designed with different doping concentrations and higher as well as lower tsi/tox ratio. All the analytical model results are verified through comparisons with TCAD Sentaurus simulation results. It is observed that the model matches quite well with TCAD device simulations.

Analytical Modeling of DG-MOSFET in Subthreshold Regime by Green’s Function Approach

In this paper, we have developed an analytical model of double gate MOSFET using Green's function approach in the subthreshold regime of operation. The exact analytical solution to 2-D Poisson's equation by Green's function approach is redefined and Fourier coefficients are calculated correctly that has a direct impact on the outcomes of the model. The approach considers 2-D mixed boundary conditions and multizone techniques while deriving potential equations. It is observed that the Green's function approach of solving 2-D Poisson's equation in both oxide and silicon region can accurately predict channel potential, subthreshold current (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub</sub> ), and subthreshold slope of both long and short channel devices designed with higher as well as lower t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">si</sub> /t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ox</sub> oxide thickness ratio.

Effect of blending polymer insulators on the improvement of the performance of poly(3-hexylthiophene) transistors

This study investigated the correlations between the microstructure and electrical properties of regioregular poly(3-hexylthiophene) (rr-P3HT) blended with polystyrene, poly(vinyl phenol), or poly(methyl methacrylate) (PMMA) thin-film transistors (TFTs). Compared with pure rr-P3HT TFT, the blended rr-P3HT TFTs exhibited superior characteristics such as higher on/off current ratio of approximately 104, lower leakage current of <10−11A, smaller sub-threshold swing of approximately 2.09V/dec, and higher mobility of approximately 8.18×10−3cm2/Vs. The suppression of the leakage current of the sub-threshold and off regimes may be attributed to the enhanced oxygen/humidity resistance of blended rr-P3HT TFTs. The evaluation of the physical properties showed that polymer insulators positively contributed to the morphology, molecular orientation, and effective conjugated length of the rr-P3HT film, thereby enhancing the device characteristics. The hybrid Al2O3/PMMA gate insulator was also utilized to apply low-voltage TFTs with rr-P3HT/polymer blends and yielded a low operation voltage of −2V.

Tuning of Multiple Parameters With a BIST System

This paper presents a low-power built-in self-test system to compensate for mismatch and variations in CMOS IC. The system is designed and compiled on a low-power field programmable analog array (FPAA) fabricated on a 350-nm CMOS process. A second-order bandpass filter is used as a device under test. A set of 12 parallel filter banks are compiled on three different FPAA chips and compensated for local mismatch and variations in the bias current, and mismatch in parasitic and routing capacitances. The bandpass filters are biased in subthreshold regime and the system of 12 parallel filter banks consumes a power of $7.072~\mu \text{W}$ . The proposed tuning algorithm reduces variation in center frequency to 5.07% compared with a variation of 10.16% when they are not tuned, variation in quality factor to 8.52% from 13.86%, and variation in the gain at the center frequency to 3.83% from 21.04%. These values are deviation of the parameters from its mean for the data taken from three different FPAA chips fabricated on the same wafer.

Ultra-sensitive suspended atomically thin-layered black phosphorus mercury sensors

The extraordinary properties of black phosphorus (BP) make it a promising candidate for next-generation transistor chemical sensors. However, BP films reported so far are supported on substrate, and substrate scattering drastically deteriorates its electrical properties. Consequentially, the potential sensing capability of intrinsic BP is highly underestimated and its sensing mechanism is masked. Additionally, the optimum sensing regime of BP remains unexplored. This article is the first demonstration of suspended BP sensor operated in subthreshold regime. BP exhibited significant enhancement of sensitivity for ultra-low-concentration mercury detection in the absence of substrate, and the sensitivity reached maximum in subthreshold regime. Without substrate scattering, the suspended BP device demonstrated 10 times lower 1/f noise which contributed to better signal-to-noise ratio. Therefore, rapid label-free trace detection of Hg2+ was achieved with detection limit of 0.01 ppb, lower than the world health organization (WHO) tolerance level (1 ppb). The time constant for ion detection extracted was 3s. Additionally, experimental results revealed that good stability, repeatability, and selectivity were achieved. BP sensors also demonstrated the ability of detecting mercury ions in environment water samples. The underling sensing mechanism of intrinsic BP was ascribed to the carrier density variation resulted from surface charge gating effect, so suspended BP in subthreshold regime with optimum gating effect demonstrated the best sensitivity. Our results show the prominent advantages of intrinsic BP as a sensing material.

Single carrier trapping and de-trapping in scaled silicon complementary metal-oxide-semiconductor field-effect transistors at low temperatures

The scaling of Silicon (Si) technology is approaching the physical limit, where various quantum effects such as direct tunnelling and quantum confinement are observed, even at room temperatures. We have measured standard complementary metal-oxide-semiconductor field-effect-transistors (CMOSFETs) with wide and short channels at low temperatures to observe single electron/hole characteristics due to local structural disturbances such as roughness and defects. In fact, we observed Coulomb blockades in sub-threshold regimes of both p-type and n-type Si CMOSFETs, showing the presence of quantum dots in the channels. The stability diagrams for the Coulomb blockade were explained by the potential minima due to poly-Si grains. We have also observed sharp current peaks at narrow bias windows at the edges of the Coulomb diamonds, showing resonant tunnelling of single carriers through charge traps.

Universal Compact Model for Thin-Film Transistors and Circuit Simulation for Low-Cost Flexible Large Area Electronics

Thin-film transistors (TFT) in hydrogenated amorphoussilicon, amorphousmetal oxide, andsmallmolecule and polymer organic semiconductors would all hold promise as potential device candidates to large area flexible electronics applications. A universal compact dc model was developed with a proper balance between the physical and mathematical approaches for these thin-film transistors (TFTs). It can capture the common key parameters used for device performance benchmarking of the different TFTs while being applicable to a wide range of TFT technologies in different materials and device structures. Based on this model, a user-friendly tool was developed to provide an interactive way for convenient parameter extraction. The model is continuous from the off-state and subthreshold regimes to the above-threshold regime, avoiding the convergence problems when being used in SPICE circuit simulations. Finally, for verification, it was implemented into a SPICE circuit simulator using Verilog-A to simulate a TFT circuit examplewith the simulated results agreeing verywell with the experimental measurements.

Quantum dynamics of intracavity third-subharmonic generation

The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.

Impact of Subthreshold Carrier Statistics on the Low-Frequency Noise in MOSFETs

Low-frequency noise analysis is being used as a method to understand the nature of carrier transport in new material-based devices and to improve the sensitivity of sensors operating in the subthreshold regime. In this paper, we show that the $(\rm{g}_{\rm m}/\rm{I}_{\rm d})^{2}$ method used in carrier number fluctuation based noise formulation needs modification in the subthreshold regime. Based on the new formulation, many published results may require reinterpretation. The new formulation is validated with data extracted from the literature for III–V, nanowire, and high-K gate-stack-based devices.

Analysis and Design of the Classical CMOS Schmitt Trigger in Subthreshold Operation

In this paper, the classical CMOS Schmitt trigger (ST) operating in the subthreshold regime is analyzed. The complete DC voltage transfer characteristic of the CMOS ST is determined. The metastable segment of the characteristic is explained in terms of the negative resistance of the NMOS and PMOS subcircuits of the ST. Small-signal analysis is carried out to determine the minimum supply voltage at which the hysteresis appears and to obtain a rough estimation of the hysteresis width. It is shown that the theoretical minimum supply voltage required to obtain hysteresis is 2ln( $2+\surd 5$ )kT/q = 75 mV at room temperature. A test chip with CMOS Schmitt triggers was designed and fabricated in a 180 nm technology in order to study their operation at supply voltages between 50 mV and 1000 mV.

A Physics-Based (Verilog-A) Compact Model for DC, Quasi-Static Transient, Small-Signal, and Noise Analysis of MOSFET-Based pH Sensors

High-resolution pH measurement is important for biomedical, food, pharmaceutical industries as well as agricultural/environmental monitoring. Among the pH-meters, FET sensors (pH-FETs) offer several advantages, such as, higher sensitivity, lower cost, and smaller size. In this paper, we develop a physics-based (Verilog-A) compact model to simulate dc, quasi-static transient, small-signal, and noise performance of pH-FET sensors. The Verilog-A implementation would allow pH-FET integration with complex signal processing circuits, and prediction of the integrated performance. The model predicts that FET thermal noise dominates in subthreshold, while FET flicker noise dominates above threshold. The minimum pH resolution is dictated by an interplay of FET and electrolyte noise sources, which are in turn functions of transistor geometry and operating condition. For a given technology node, if the sensor is designed to operate in subthreshold regime, pH-FET with shorter but wider channel has better pH resolution. In contrast, for sensor designed to operate in the inversion regime, longer and wider channel is preferred. Finally, we demonstrate the utility of the Verilog-A implementation by circuit simulation of a low-power sensor interface.

Physics-Based Analytical Model for Input, Output, and Reverse Capacitance of a GaN HEMT With the Field-Plate Structure

This paper presents an analytical model for input, output, and reverse capacitance of a normally on AlGaN/GaN high-electron mobility transistor (HEMT) with a gate field-plate structure, when the device is in the subthreshold regime. Together with the existing model for the output I–V characteristics, the proposed capacitance model provides the complete set of analytical equations that relate the physical design parameters to the electrical characteristics of the device. The model was verified by the experimental characterization of a HEMT. In comparison to the physics-based models implemented in Finite Element Analysis tools, the obtained capacitance model has substantially lower level of complexity and, therefore, it is more suitable for implementation into iterative design optimization algorithms. In order to verify the proposed model for such usage, the prototype of a high-frequency buck converter was built, using previously modeled GaN HEMT as the main switch. The hybrid analytical-behavioral power loss model of a high-frequency buck converter was implemented into Simplorer simulation tool, using the proposed physics-based model as the device description for the capacitive part. The efficiency measurements showed good agreement with the simulation results, even at 20 MHz of switching frequency in the low range of the output power.

Air-stable vapor phase sensing of ammonia in sub-threshold regime of poly(2,5-bis(3-tetradecylthiophen-2yl)thieno(3,2-b)thiophene) based polymer thin-film transistor

In the present study, device geometry having top contact bottom gated poly(2,5-bis(3-tetradecylthiophen-2yl)thieno(3,2-b)thiophene) (PBTTT) based polymer thin film transistor (PTFT) is reported to measure the changes in electrical responses with the exposure to various concentrations of ammonia vapor at room temperature. PTFT is preferred over other electronic devices due to its multi-parameter characteristics to explore gas sensing capabilities. A facile floating–film transfer method (FTM) is used to prepare an active layer of PTFT by forming optimized thin layer of PBTTT film having a thickness of ∼25nm. Exposure to various concentrations of ammonia vapor, device parameters like I/O characteristics, mobility, threshold voltage, and trap density are found to change significantly. As PTFT is exposed to 100ppm ammonia vapor a 70% reduction in mobility is observed whereas threshold voltage shifted to more negative from −17.62V to −23.64V. Better sensing capabilities with a detection limit of 0.33ppm, fast response and recovery of exposed ammonia vapor are observed, when PTFT is operated in sub-threshold regime rather than the cut-off or saturated regime. All the electrical characterizations for the sensing purpose are carried out in ambient but in a closed chamber. Device shows enormous potential for ammonia sensing for real and environmental applications.

Analysis and Design of Power Harvesting Circuits for Ultra-Low Power Applications

This paper presents an analytical model for power harvester circuits used in Ultra-low power applications. Assuming that the MOS devices of the circuit fully operate in the Sub-threshold regime in both forward and reverse regions, closed-form equations for important properties of the rectifier circuit such as output voltage, efficiency and input resistance are derived. The model includes the effect of the compensation voltage on the circuit behavior. There is a good agreement between the simulation results and the model. In addition, the contour plots needed to simultaneously optimize the matching network and the rectifier circuit are derived by the resulting equations. A 50-Stage rectifier was fabricated in a 180-nm standard CMOS Process. The proposed model is verified with the measurement results. The model has a maximum error of 10% in comparison with the circuit simulation, and a maximum error of 12% with the measured values.

Impact of contact resistance on the electrical properties of MoS2 transistors at practical operating temperatures.

Molybdenum disulphide (MoS2) is currently regarded as a promising material for the next generation of electronic and optoelectronic devices. However, several issues need to be addressed to fully exploit its potential for field effect transistor (FET) applications. In this context, the contact resistance, RC, associated with the Schottky barrier between source/drain metals and MoS2 currently represents one of the main limiting factors for suitable device performance. Furthermore, to gain a deeper understanding of MoS2 FETs under practical operating conditions, it is necessary to investigate the temperature dependence of the main electrical parameters, such as the field effect mobility (μ) and the threshold voltage (Vth). This paper reports a detailed electrical characterization of back-gated multilayer MoS2 transistors with Ni source/drain contacts at temperatures from T = 298 to 373 K, i.e., the expected range for transistor operation in circuits/systems, considering heating effects due to inefficient power dissipation. From the analysis of the transfer characteristics (ID−VG) in the subthreshold regime, the Schottky barrier height (ΦB ≈ 0.18 eV) associated with the Ni/MoS2 contact was evaluated. The resulting contact resistance in the on-state (electron accumulation in the channel) was also determined and it was found to increase with T as RC proportional to T3.1. The contribution of RC to the extraction of μ and Vth was evaluated, showing a more than 10% underestimation of μ when the effect of RC is neglected, whereas the effect on Vth is less significant. The temperature dependence of μ and Vth was also investigated. A decrease of μ proportional to 1/Tα with α = 1.4 ± 0.3 was found, indicating scattering by optical phonons as the main limiting mechanism for mobility above room temperature. The value of Vth showed a large negative shift (about 6 V) increasing the temperature from 298 to 373 K, which was explained in terms of electron trapping at MoS2/SiO2 interface states.

Extended Modal Gain Measurement in DFB Laser Diodes

A practical method is proposed for complete gain measurement in distributed feedback (DFB) laser diodes. It is non-destructive and does not require any reference device. It includes the whole range of continuous gain values, from its minimum to threshold, passing through the transparency condition. The method requires a single absolute gain measurement for calibration. An example is reported for a DFB preserving Fabry–Perot multi-modes in the sub-threshold regime.

An Ultralow-Voltage Energy-Efficient Level Shifter

This brief presents an energy-efficient level shifter (LS) able to convert extremely low level input voltages to the nominal voltage domain. To obtain low static power consumption, the proposed architecture is based on the single-stage differential-cascode-voltage-switch scheme. Moreover, it exploits self-adapting pull-up networks to increase the switching speed and to reduce the dynamic energy consumption, while a split input inverting buffer is used as the output stage to further improve energy efficiency. When implemented in a commercial 180-nm CMOS process, the proposed design can up-convert from the deep subthreshold regime (sub-100 mV) to the nominal supply voltage (1.8 V). For the target voltage level conversion from 0.4 to 1.8 V, our LS exhibits an average propagation delay of 31.7 ns, an average static power of less than 60 pW, and an energy per transition of 173 fJ, as experimentally measured across the test chips.

A 3μW Low-Power CMOS Class-AB Bilateral Current Mirror for Low-Voltage Applications

This paper presents a compact low-power bidirectional current mirror suitable for low-voltage applications. The key element is the use of a CMOS complementary input stage working in subthreshold regime; which allows setting a reduced bias current through the mirror. The circuit was simulated using LTSpice and presents class AB operation with a THD of 1% at 1MHz. The power consumption is close to 3μW as shown by simulations and experimental data from a fabricated prototype using 0.5µm CMOS technology.

Modeling and analysis of sub-surface leakage current in nano-MOSFET under cutoff regime

The high leakage current in nano-meter regimes is becoming a significant portion of power dissipation in nano-MOSFET circuits as threshold voltage, channel length, and gate oxide thickness are scaled down to nano-meter range. Precise leakage current valuation and meticulous modeling of the same at nano-meter technology scale is an increasingly a critical work in designing the low power nano-MOSFET circuits. We present a specific compact model for sub-threshold regime leakage current in bulk driven nano-MOSFETs. The proposed logical model is instigated and executed into the latest updated PTM bulk nano-MOSFET model and is found to be in decent accord with technology-CAD simulation data. This paper also reviews various transistor intrinsic leakage mechanisms for nano-MOSFET exclusively in weak inversion, like drain-induced barricade lowering (DIBL), gate-induced drain leakage (GIDL), gate oxide tunneling (GOT) leakage etc. The root cause of the sub-surface leakage current is mainly due to the nano-scale short channel length causing source–drain coupling even in sub-threshold domain. Consequences leading to carriers triumphing the barricade between the source and drain. The enhanced model effectively considers the following parameter dependence in the account for better-quality value-added results like drain-to-source bias (VDS), gate-to-source bias (VGS), channel length (LG), source/drain junction depth (Xj), bulk doping concentration (NBULK), and operating temperature (Top).