Boltzmann Constant Research Articles

Constructal Optimizations of Line-to-Line Vascular Channels with Turbulent Convection Heat Transfer.

The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of LVCs with any order are conducted by taking the angles at bifurcations as the optimization variables. The heat flux on the channel wall per unit length is fixed and uniform. The areas occupied by vasculature and the total volumes of channels are fixed. The analytical expressions of the optimal angles, dimensionless total entropy generation rate and entropy generation number (EGN) of LVCs with any order versus dimensionless mass flow rate are obtained, respectively. The results indicate that the dimensionless total entropy generation rate of LVCs with any order can be significantly decreased by optimizing the angles of LVCs, which is significantly more when the order of LVCs is higher. As the dimensionless mass flow rate increases, the optimal angles of LVCs with any order remain unchanged first, then the optimal angles at the entrance (root) increase, and the other optimal angles decrease continuously and finally tend to the respective stable values. The optimal angles of LVCs continue to increase from the entrance to the outlet (crown), i.e., the LVCs with a certain order gradually spread out from the root to the crown. The dimensionless total entropy generation rate and EGN of LVCs first decrease and then increase with the growth of the dimensionless mass flow rate. There is optimal dimensionless mass flow rate, making the dimensionless total entropy generation rate and the EGN reach their respective minimums. The results obtained herein can provide some new theoretical guidelines of thermal design and management for the practical applications of LVCs.

MEMS Thermocouple Sensor Based on 4H-Silicon-Carbide-On-Insulator (4H-SiCOI)

With the high thermal conductivity and breakdown voltage, silicon carbide (SiC) has been treated as a promising material to work in harsh environment especially high temperature. However, due to its chemical inertness and wide band-gap, it is difficult to achieve the ion implantation, etching and good ohmic contact. In this study, silicon carbide on insulator (4H-SiCOI) is applied to fabricate MEMS thermocouple sensor, which can simultaneously compatible with bulk silicon CMOS process. The stress and temperature distribution of the sensor was simulated by COMSOL. After optimized the process parameters, the sensor based on 4H-SiCOI was successfully fabricated. Preliminary test results demonstrated the sensor shows good sensitivity about 1.44 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times 10^{-{8}}\,\,{V}{m}^{{{2}}}/{W}$ </tex-math></inline-formula> and response time of 3.24ms, which also keeps good linearity and repeatability. This sensor can satisfy the needs of fast and high precision heat detection and our work may have a meaningful reference value for other same type SiC-based MEMS thermocouple sensor design and preparation.

Nanoscale Conductive Sheets in Ferroelectric BaTiO3: Large Hall Electron Mobilities at Head-to-Head Domain Walls

Strongly charged head-to-head (H2H) domain walls (DWs) that are purposely engineered along the [110] crystallographic orientation into ferroelectric BaTiO$_3$ single crystals have been proposed as novel 2-dimensional electron gases (2DEGs) due to their significant domain wall conductivity (DWC). Here, we quantify these 2DEG properties through dedicated Hall-transport measurements in van-der-Pauw 4-point geometry at room temperature, finding the electron mobility to reach around 400~cm$^2$(Vs)$^{-1}$, while the 2-dimensional charge density amounts to ~7$\times$10$^3$cm$^{-2}$. We underline the necessity to take account of thermal and geometrical-misalignment offset voltages by evaluating the Hall resistance under magnetic-field sweeps, since otherwise dramatic errors of several hundred percent in the derived mobility and charge density values can occur. Apart from the specific characterization of the conducting BaTiO$_3$ DW, we propose the method as an easy and fast way to quantitatively characterize ferroic conducting DWs, complementary to previously proposed scanning-probe-based Hall-potential analyses.

Power System Planning Assessment for Optimizing Renewable Energy Integration in the Maluku Electricity System

The planning of electrical power systems in remote island areas poses a few challenges, such as requiring many load centers, various energy sources, and certain geographical conditions, which leads to inefficiencies in energy production. For this reason, it is necessary to plan an electrical transmission system to efficiently transfer the power between load centers. Previous research has found that the completion of the most economical power system will be achieved in 2050 on the condition that the Ambon, Seram, Haruku, and Saparua (Ambon-SHS) systems are interconnected in 2025. Providing complementary support, this paper conducts a power system analysis to assess the proposed interconnection system in Maluku Island, which has several islands, small load centers, and local renewable energy resources. The power system analysis was performed using DIgSILENT PowerFactory and was carried out every 5 years of the system planning period until 2050. The results show that the design of the obtained transmission system meets the standard security criteria, which include thermal loading and voltage, being under both normal and N-1 contingency conditions, a short-circuit current, voltage stability, frequency stability, and transient stability. Finally, this paper demonstrates that the proposed plan is economically and technically feasible.

(Invited) Durability of Electrolyte Supported Solid Oxide Cells for Steam Electrolysis: Results from Cell Testing in the 20,000 h to 50,000 Hours Range

There is a current fast development of water/steam electrolysis for the production of hydrogen from renewable energy sources. (Multi) MW power demonstration units using the different (low and high temperature) technologies are, e.g., subject of the R&D project H2Giga funded by the German Federal Ministry of Education and Research /1/. Steam electrolysis with solid oxide cells (SOC) is characterised by a high energy-conversion efficiency, notably if steam is available, such as via a heat source of moderate temperature for steam generation. Approaches for a matching to a fluctuating load, important in the context of operation with renewable energy sources, are also under development with the SOC technology /2/.For the SOC electrolysers, durability analysis of the cells in a time scale appropriate for application remains an important development step. Cell (or short stack) testing allows a rather precise control of the cell temperature which facilitates quantification of degradation for the practically required degradation rates well below 10 mV/1000 h (cf. /3/). In this contribution, our testing results will be updated, with up to about 50,000 h operation using electrolyte supported cells (ESC) with Ni/GDC hydrogen electrodes and different types of electrolyte (10Sc1CeSZ, 6Sc1CeSZ, 3YSZ). As reference for cell durability serves a 23,000 h steam electrolysis test with a cell with 6Sc1CeSZ electrolyte /4/. However, cells with the known robust 3YSZ electrolyte seem to yield a comparably low long-term degradation, together with better initial stability /5/. The use of an electrolyte of high ionic conductivity, 10Sc1CeSZ, allows a relatively low initial temperature (<800°C) for a cell voltage close to the thermal neutral voltage for 0.6 Acm-2 current density. This, in turn, leaves a wide temperature margin for compensation of voltage degradation via a temperature increase (cf. initial period of the test in /3/). The results from the durability tests serve as examples for a large degree of SOFC/SOEC reversibility achievable with the ESC. Moreover, the relatively thick electrolyte layer of the ESC with its large ohmic resistance comes along with a high ohmic contribution in the overall degradation in most tests. The different degradation contributions were separated with in-situ impedance spectroscopy without interrupting the DC current flow.

Spectral Properties and Hybrid Jet Model Constraints of Fermi GRB 210610B

The jet composition of gamma-ray bursts (GRBs) is still an open question and the energy spectrum characteristics can provide us with evidence. GRB 210610B is a special burst with low-energy indices that are all greater than the synchrotron cutoff. We first use two empirical models, Band and CPL, and one physics model, a blackbody, to perform time-resolved spectral analysis on GRB 210610B and find that about 76.47% of the spectra need an addition thermal component to obtain a better fit. Moreover, these spectra could be well fitted by a multicolor blackbody (mBB) and the synchrotron model. We then adopt the hybrid jet model proposed by Gao & Zhang to perform a “top-down” approach to diagnose the photospheric properties (η and σ 0) of the central engine from observational data. We find both the dimensionless entropy η and the magnetization parameters (1 + σ 0) are greater than 1, indicating that the Poynting flux component may play an important role in addition to the hot fireball component. Our analysis also shows that most of the spectra have a magnetization parameter (1 + σ 15) ≃ 1 at ∼1015 cm, suggesting that nonthermal emission may originate from internal shocks. Furthermore, we find that α and E p show different time evolution behaviors: α exhibits a “hard-to-soft” behavior and moderately correlates with flux, while E p exhibits a “tracking” behavior. The magnetic field strength B and the mBB parameter kT max also show a “tracking” behavior. Our results suggest that the empirical model CPL may be interpreted by an mBB.

Real and imaginary permittivity measured by thermal noise dielectric spectroscopy

This paper demonstrates that both real and imaginary parts of dielectric permittivity in a kHz frequency range can be determined from the thermal noise voltage spectra. The proposed method, termed as thermal noise dielectric spectroscopy, relies on the set of calibration measurements of gauge resistors and capacitors. This method has a great potential for investigations of strongly nonlinear dielectric materials whenever the initial permittivity is of interest because the thermal noise method probes the permittivity by an almost zero electric field. Here, we tested this method by measuring dielectric spectra of 100 nm thin film of paraelectric SrTiO3 in a thermal noise setup in which the film is effectively probed by voltages of the order of nanovolts. For the sake of comparison, the permittivity of the same SrTiO3 thin film has been also measured using the standard impedance analyzer with the probing AC voltage of 10 mV. Agreement between methods is remarkable for both real and imaginary parts of the permittivity. Results strongly suggest that the proposed technique is broadly applicable for investigation of the frequency and temperature dependence of the complex permittivity of nanoscale dielectric materials.

A novel PV array reconfiguration approach to mitigate non-uniform irradiation effect

The extraction of power at global maximum power point (GMPP) has been affected due to non-uniform row-current generation leading to the formation of multiple peaks in power-voltage (P-V) curve. This issue booms out due to set of factors referred to as partial shading condition (PSC). To root-out this issue, puzzle-game based strategies were developed based on physical relocation of shaded modules with the unshaded one. This has a limitation when considering the size as a parameter which is non-effective for larger shade-dispersion. Thus, to alleviate this issue, this research paper intends to execute a novel reconfiguration topology based on idea of permutation and combination (P-C). This novel metaheuristic approach is focussed on building a fitness function in terms of efficiency (Ƞ), fill-factor (FF) and power loss (PLOSS). A connection list has been prepared to evaluate for optimal combination of solar modules. Hence, this approach excels in providing an optimum solar array attenuating the complexity of the photovoltaic (PV) system. The effectiveness of this approach has been validated through MATLAB tool on 4 × 4, 6 × 4 and 9 × 9 solar array size under various shading patterns. To bring out more efficacy, this suggested novel approach has been elaborately compared with traditional Total cross tied (TCT) topology and two other puzzle-based topology Ken-Ken (K-K) and L-shape (L-S) topology for 4 × 4 solar array size on the basis of 16 performance parameters; maximum voltage (VMAX), maximum current (IMAX), GMPP, local maximum power point (LMPP; its values and number of peaks generated on the P-V curve), misleading power loss (MLPL), mismatch loss (MLOSS), current and voltage loss (ILOSS, VLOSS), PLOSS, execution ratio (ER), Ƞ, FF, %power improvement (%PI), thermal voltage (TV) and power enhancement ratio (PER). Results for 4 × 4 solar array size portray that P-C has enhanced GMPP by 5.64 W, 5.64 W and 6.61 W reducing PLOSS by 7%, 6% and 8.26% respectively over L-S, K-K and TCT under border shading. Validation of the novel P-C for 6 × 4 solar array size has been done with TCT and L-S. Its results conclude that GMPP of P-C is incremented by 12.99 W and 0.70 W reducing the PLOSS by 11.16% and 0.99% respectively over TCT and L-S under corner shading. Further, the novel P-C for 9 × 9 solar array size has been validated with TCT, K-K, L-S, Ancient Chinese (A-C) and Skyscraper (S-S) topologies. GMPP of the novel P-C is improved by 16.19 W, 12.34 W, 12.34 W, 12.11 W and 2.75 W minimizing the PLOSS by 5.80%, 5.75%, 5.75%, 5.73% and 4.23% over TCT, K-K, L-S, A-C and S-S under zigzag shading. The comparative results under all the three considered solar array size strongly suggests the increased ability of the proposed novel P-C approach in enhancing the performance parameters and an effective shade dispersion over the entire PV array under PSC as compared to other considered reconfigurations.

Role of Ions in Hydrogels with an Ionic Seebeck Coefficient of 52.9 mV K-1.

Ionic thermoelectric (i-TE) material with mobile ions as charge carriers has the potential to generate large thermal voltages at low operating temperatures. This study highlights the role of ions in i-TE hydrogels employing a poly(vinyl alcohol) (PVA) polymer matrix and a number of ion providers, e.g., KOH, KNO3, KCl, KBr, NaI, KI, and CsI. The relationship between the intrinsic physical parameters of the ion and the thermoelectric performance is established, indicating the ability to influence the hydrogen bond by the ion is a crucial factor. Among these i-TE hydrogels, the PVA/CsI hydrogel exhibits the largest ionic Seebeck coefficient, reaching 52.9 mV K-1, which is the largest of all i-TE materials reported to date. In addition, our work demonstrates the influence of ions on polymer configuration and provides an avenue for ion selection in the Soret effect in ionic thermoelectrics.

Magnetic properties of a capped kagome molecule with 60 quantum spins

We compute ground-state properties of the isotropic, antiferromagnetic Heisenberg model on the sodalite cage geometry. This is a 60-spin spherical molecule with 24 vertex-sharing tetrahedra which can be regarded as a molecular analogue of a capped kagome lattice and which has been synthesized with high-spin rare-earth atoms. Here, we focus on the S=1/2S=1/2 case where quantum effects are strongest. We employ the SU(2)-symmetric density-matrix renormalization group (DMRG). We find a threefold degenerate ground state that breaks the spatial symmetry and that splits up the molecule into three large parts which are almost decoupled from each other. This stands in sharp contrast to the behaviour of most known spherical molecules. On a methodological level, the disconnection leads to ``glassy dynamics’’ within the DMRG that cannot be targeted via standard techniques. In the presence of finite magnetic fields, we find broad magnetization plateaus at 4/5, 3/5, and 1/5 of the saturation, which one can understand in terms of localized magnons, singlets, and doublets which are again nearly decoupled from each other. At the saturation field, the zero-point entropy is S=\ln(182)\approx 5.2S=ln(182)≈5.2 in units of the Boltzmann constant.

An advanced HBNP multi-level inverter for the performance enhancement with reduced components

ABSTRACT This article proposed an advanced three-phase multilevel inverter called the H-Bridge Neutral Point (HBNP) Inverter, with a minimum number of components. This inverter is designed to generate five-level output voltage using a single solar system in each phase, making it suitable for low-, medium-, and high-power applications like AC drives, grid integration of renewable energy sources, electric vehicles, and high voltage DC and AC transmission systems, etc. The proposed circuit configuration has reduced gate driver circuits, less capacitors, fewer input sources, modularity in structure, and better THD. Furthermore, the hybrid PWM control technique provides switching signals and ensures that all switches have equal conduction intervals. All of the switches have the same temperatures and voltage sharing, indicating a simpler thermal design and DC bus voltage balancing. The proposed and existing topologies are validated using MATLAB Simulink, and the proposed topology prototype is implemented in the laboratory.

Set-up for observation thermal voltage noise and determination of absolute temperature and Boltzmann constant

We describe a set-up for measurement of the absolute zero by Johnson–Nyquist thermal noise which can be performed within a week in every high-school or university. Necessary electronic components and technical guidelines for the construction of this noise thermometer are given. The operating temperature used is in the tea cup range from ice to boiling water and in this sense the set-up can be given in the hands of every high school and university physics student. The measurement requires a standard multi-meter with thermocouple and voltage probe and gives excellent for education purposes percent accuracy. The explanation is oriented to university level but due to the simplicity of the explanation motivated high-school students can follow the explanation derivation of the used formulas for determination of the absolute zero and the Boltzmann constant. As a by-product our set-up gives a new method for the determination of the spectral density of the voltage e N and current noise i N of operational amplifiers.

Thermo-electro-environmental analysis of a photovoltaic solar panel using machine learning and real-time data for smart and sustainable energy generation

The impact of meteorological parameters, including ambient temperature, wind velocity, ambient relative humidity, and solar radiation on photocurrent and thermal voltage of diode, as two main thermo-electrical parameters of a solar panel, is found. For this purpose, the experimental data obtained during a year, in addition to the post-processed images captured by an infrared thermal imaging camera, are used, and models for performance prediction by the artificial neural network are developed and validated. In addition, the impact of photocurrent and thermal voltage of diode on CO2 saving of the system is found. According to the results, for the investigated 320W polycrystalline panel, with 200.0% increase in the range of 500–1500 W m−2, solar radiation has the strongest impact on photocurrent. Moreover, the most effective meteorological parameter on the thermal voltage of diode is ambient temperature. Changing ambient temperature from 27 to 47 °C is accompanied by 9.36% growth in that parameter. The conducted sensitivity analysis also reveals that between photocurrent and thermal voltage of diode, the former is a more effective parameter on CO2 emission reduction of the system. When photocurrent values are 20% lower and 20% higher than the base case, the amounts of CO2 saving are 18.0% smaller and 14.6% greater, respectively. It means 32.6% variation within the range.

Li-stuffed garnet electrolytes: structure, ionic conductivity, chemical stability, interface, and applications

Current lithium-ion batteries have been widely used in portable electronic devices, electric vehicles, and peak power demand. However, the organic liquid electrolytes used in the lithium-ion battery are flammable and not stable in contact with elemental lithium and at a higher voltage. To eliminate the safety and instability issues, solid-state (ceramic) electrolytes have attracted enormous interest worldwide, owing to their thermal and high voltage stability. Among all the solid-state electrolytes known today, the Li-stuffed garnet is one of the most promising electrolytes due to its physical and chemical properties such as high total Li-ion conductivity at room temperature, chemical stability with elemental lithium and high voltage lithium cathodes, and high electrochemical stability window (6 V vs. Li+/Li). In this short review, we provide an overview of Li-stuffed garnet electrolytes with a focus on their structure, ionic conductivity, transport mechanism, chemical stability, and battery applications.

The AC amplitude and channel characterization of high-resolution digitizers

High-resolution (24-bit) ADC based sampling devices e.g. NI PXI 5922 and NI PXI 4461 are usually used for precise electric power measurement purpose so it is required to characterize them in a proper way. According to that, several measurement techniques are proposed to characterize ac amplitude and channel characteristics at the maximum frequency of up to 100 kHz. An automated test and calibration system based on a planar multijunction thermal voltage converter and a modular electronic instrumentation platform has been developed. Furthermore, two ADCs, i.e. NI PXI 5922 and NI PXI 4461 have been compared with reference standard (Swerlein algorithm) to investigate their precision in RMS amplitude measurement of ac signals. In addition, this paper presents the PXI digitizers’ channel characterization in both sinusoidal and non-sinusoidal regime as the main contribution which results in comprehensive insight into digitizers’ performances and their mutual comparison. Accordingly, relevant uncertainty analysis is presented as well.

The electrochemical impedance spectrum of asymmetric electrolytes across low to moderate frequencies

• New mathematical analysis for the electrochemical impedance spectrum of asymmetric electrolytes. • Double plateau behavior in the real part of impedance predicted across low to moderate frequencies. • Low frequency response is caused transient bulk diffusion, or concentration polarization, of salt across an electrochemical cell. We develop new mathematical expressions for the electrochemical impedance spectrum of an asymmetric electrolyte. Specifically, we consider the Poisson-Nernst-Planck (PNP) equations governing ion transport in a binary asymmetric electrolyte with unequal valences and diffusivities, flanked by planar, parallel, blocking electrodes. The electrodes are subject to an oscillating voltage of small amplitude comparable to the thermal voltage scale. We further consider the limit practically applicable to liquid electrolytes of thin Debye layers ∊ = 1 / ( κ L ) ≪ 1 , where κ - 1 is the Debye screening length and L is the length of the half cell. The impedance is then obtained from the current in the external circuit, defined as the rate of change of electric field at either electrode. We identify two distinct asymptotic regimes for the frequency ( ω ) in the limit ∊ → 0 : low frequencies, on the order of the inverse bulk diffusion time ω = O ( D A / L 2 ) ; and moderate frequencies, on the order of the inverse RC charging time scale ω = O ( D A κ / L ) . Here D A = ( z + + z - ) D + D - / ( z + D + + z - D - ) is the ambipolar diffusion coefficient of the salt, z ± are the ionic valences, and D ± are the ionic diffusivities. Our analysis provides new, concise expressions for the impedance at low and moderate frequencies, that account for ionic valence asymmetry. Further, in the moderate frequency analysis, higher order contributions (in ∊ ) to the impedance reveal that the real part (i.e. the resistance) appears to diverge as ω - 1 / 2 in the limit ω L / ( κ D A ) → 0 , akin to a semi-infinite Warburg element. We determine that this occurs due to the existence of oscillating diffusion layers, O ( ∊ 1 / 2 L ) in width, that bridge the ion transport between the O ( ∊ L ) wide Debye layers adjacent to each electrode and the O ( L ) wide bulk electro-neutral electrolyte. In the low frequency regime, however, these diffusion layers relax, and effectively merge across the bulk of the cell; consequently, the resistance spectrum attains a plateau in the limit of zero frequency ω L 2 / D A → 0 . Thus, our asymptotic analysis discerns the electrochemical processes that dictate the impedance of asymmetric electrolytes at the low and moderate frequency regimes.

A model-based approach for detecting and identifying faults on the D.C. side of a P.V. system using electrical signatures from I-V characteristics.

With the development of distributed generation and the corresponding importance of the P.V. (photovoltaic) system, it is desired to operate a P.V. system efficiently and reliably. To ensure such an operation, a monitoring system is required to diagnose the health of the system. This paper aims to analyze a P.V. system under various operating conditions to identify parameters-derived from the I-V (current-voltage) characteristics of the P.V. system-that could serve as electrical signatures to various faulty operations and facilitate in devising a monitoring algorithm for the system. A model-based approach has been adopted to represent a P.V. system, using a one-diode model of a practical P.V. cell, developed in MATLAB/Simulink. The modelled system comprises two arrays, while each array has two panels in series. It was simulated for various operating conditions: healthy condition represented by STC (Standard Testing Condition), O.C. (open-circuited), soiling, P.S. (partial-shading), H.S. (panels hotspots) and P.D. (panels degradation) conditions. For the analysis of I-V curves under these conditions, six derived parameters were selected: Vte (equivalent thermal voltage), MCPF (maximum current point factor), Ri (currents ratio), S (slope), and Dv and Di (voltages and currents differences, respectively). Using these parameters, data of the actual system under various conditions were compared with its model-generated data for healthy operating conditions. Thresholds were set for each parameter's value to mark normal operation range. It was observed that almost each considered fault creates a unique combination of sensitive parameters whose values exceeds the pre-defined thresholds, creating an electrical signature that will appear only when the corresponding conditions on the system are achieved. Based on these signatures, an algorithm has been proposed in this study which aims to identify and classify the considered faults. In comparison to other such studies, this work has been focused on those sensitive parameters for faults identification which shows greater sensitivity and contribute more to creation of unique sets of sensitive parameters for considered faults.

Experimental Study of Entropy Generation of Nanofluid Flow in Minichannel

This study investigates the effects of ZnO, , and particles in the water-based fluid on entropy generation minimization in a minichannel heat exchanger. Distilled water has been chosen as the base fluid for nanoparticle volume concentration of 0.5% under the laminar and turbulent regime, steady-state flow, and the constant wall temperature. Dynamic viscosity, thermal conductivity, heat transfer, pressure drop, and total entropy generation rates of nanofluids have been experimentally analyzed in the minichannel (stainless steel), which has an inner diameter of and length of 20 cm, at the constant wall temperature (283 K). The nanofluid mixtures have been studied at different flow rates (from 10 to 50 ml/min) at the constant inlet (323 K) and constant channel wall temperature (283 K). The thermal performance, the pressure drop, and total entropy generation rates of the fluids have been compared for three different types of nanofluids. Maximum heat transfer enhancement of 16.04% was obtained using water-based . Results have shown that three nanofluids have less dimensionless entropy generation than pure water. In addition, compared to pure water with these three nanofluids, the minimum value of the total entropy generation has been obtained for with 5.54%.

Universal Constants as Manifestations of Relativity

We study the possible interpretation of the "universal constants" by the classification of J.-M. Lévy-Leblond. The Planck constant and the speed of light in vacuum are the most common examples of constants of this type. Using Fock’s principle of the relativity w.r.t. observation means, we show that these two constants can be viewed as manifestations of certain relativity. We also show that there is a possibility to interpret the Boltzmann constant in a similar way, and make some comments about the relativistic interpretation of the constant spacetime curvature and gravitational constant G.

A Threshold Voltage Definition Based on a Standardized Charge Versus Voltage Relationship

Threshold voltage defined by a band bending of twice the substrate intrinsic-to-Fermi level difference has been widely accepted. However, there are shortcomings with this analytical definition. Since the inversion condition is governed by the substrate Fermi level (i.e., majority carrier density per volume), inversion carrier density per area at threshold inadequately depends on substrate doping and temperature. Another problem is that the definition is not applicable to fully depleted thin body devices, such as FinFETs and silicon-on-insulator FETs, widely used today. To solve these problems, a new definition of threshold voltage is proposed, which is based on a standardized charge versus voltage relationship of ideal metal-oxide-semiconductor capacitors. Threshold voltage is specified by a threshold inversion carrier density per area, which is a simple function of gate oxide capacitance and thermal voltage. Dependence of the proposed threshold voltage on substrate doping, body thickness, and temperature for both bulk and double-gate FETs is discussed using semi-classical analytical equations.