This lecture covers field-effect transistor (FET) reviews, the motivation for tunnel field-effect transistors (TFETs), device design and simulation, relevant literature, and simulation results. The results show that subthreshold swing (SS) of 6.4 mV/dec and on/off current ratio (Ion/Ioff) of >25,000 can be achieved with a graphene nanoribbon TFET with channel length of 40nm, width of 5nm, drain bias of 0.1V, and doping of 0.24eV. SS and Ion/Ioff vary inversely and exponentially with width, positively and logarithmically with length, and positively and exponentially with doping up to 0.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
We propose a phase-locked loop (PLL) architecture, which reduces the double frequency ripple without increasing the order of loop filter. Proposed architecture uses quadrature numerically–controlled oscillator (NCO) to provide two output signals with phase difference of π/2. One of them is subtracted from the input signal before multiplying with the other output of NCO. The system also provides stability in case the input signal has noise in amplitude or phase. The proposed structure is implemented using field programmable gate array (FPGA), which dissipates 15.44mw and works at clock frequency of 155.8 MHz.
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...Victor Solntsev
The equations that describe nonlinear nonstationary processes in carcinotrode (backward- wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscil- lations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self- modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode–grid static field.
Development of Improved Diode Clamped Multilevel Inverter Using Optimized Sel...eeiej_journal
In this paper the role of Selective Harmonic Elimination (SHE) is presented for diode clamped twelve-level multilevel inverter (DCMLI) based on dog leg optimization algorithm. Non-linear equations has been solved to eliminate specific low order harmonics, using the developed DOP algorithm, while at the same time the fundamental component is retained efficiently. The non-linear nature of transcendental equation provide multiple or even no solution for a particular modulation index. The proposed optimization method solving the nonlinear transcendental equations providing all possible solutions. The paper also showing the comparison between different modulation techniques including the proposed method. The entire system has been simulated using MATLAB/Simulink. Simulation results confirm the effectiveness with negligible
THD.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
We propose a phase-locked loop (PLL) architecture, which reduces the double frequency ripple without increasing the order of loop filter. Proposed architecture uses quadrature numerically–controlled oscillator (NCO) to provide two output signals with phase difference of π/2. One of them is subtracted from the input signal before multiplying with the other output of NCO. The system also provides stability in case the input signal has noise in amplitude or phase. The proposed structure is implemented using field programmable gate array (FPGA), which dissipates 15.44mw and works at clock frequency of 155.8 MHz.
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...Victor Solntsev
The equations that describe nonlinear nonstationary processes in carcinotrode (backward- wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscil- lations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self- modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode–grid static field.
Development of Improved Diode Clamped Multilevel Inverter Using Optimized Sel...eeiej_journal
In this paper the role of Selective Harmonic Elimination (SHE) is presented for diode clamped twelve-level multilevel inverter (DCMLI) based on dog leg optimization algorithm. Non-linear equations has been solved to eliminate specific low order harmonics, using the developed DOP algorithm, while at the same time the fundamental component is retained efficiently. The non-linear nature of transcendental equation provide multiple or even no solution for a particular modulation index. The proposed optimization method solving the nonlinear transcendental equations providing all possible solutions. The paper also showing the comparison between different modulation techniques including the proposed method. The entire system has been simulated using MATLAB/Simulink. Simulation results confirm the effectiveness with negligible
THD.
Threshold voltage model for hetero-gate-dielectric tunneling field effect tra...IJECEIAES
In this paper, a two dimensional analytical model of the threshold voltage for HGD TFET structure has been proposed. We have also presented the analytical models for the tunneling width and the channel potential. The potential model is used to develop the physics based model of threshold voltage by exploring the transition between linear to exponential dependence of drain current on the gate bias. The proposed model depends on the drain voltage, gate dielectric near the source and drain, silicon film thickness, work function of gate metal and oxide thickness. The accuracy of the proposed model is verified by simulation results of 2-D ATLAS simulator. Due to the reduction of the equivalent oxide thickness, the coupling between the gate and the channel junction enhances which results in lower threshold voltage. Tunneling width becomes narrower at a given gate voltage for the optimum channel concentration of 10 16 /cm 3 . The higher concentration in the source (N s ) causes a steep bending in the conduction and valence bands compared to the lower concentration which results in smaller tunneling width at the source-channel interface.
A Plasma Tweeter is an audio device which uses a pair of electrodes as a source of sound. It has a clear reproduction and Omni directional radiation pattern. A plasma tweeter has a better frequency response than a conventional speaker and does not involve any moving part (diaphragm) and thus has less reverberation and no wear and tear. Plasma tweeters invented earlier were very expensive. This paper presents a plasma audio system which is making the regular audio system more efficient because of the use of the latest plasma tweeter. Here the objective is to create a low cost and more efficient version of the most speakers invented till now with the complete audio system.
A.) Comparison of Voltammetry to Other Electrochemical Methods
1.) Voltammetry: electrochemical method in which information about an analyte is
obtained by measuring current (i) as a function of applied potential
- only a small amount of sample (analyte) is used
Instrumentation – Three electrodes in solution containing analyte
Working electrode: microelectrode whose potential is varied with time
Reference electrode: potential remains constant (Ag/AgCl electrode or calomel)
Counter electrode: Hg or Pt that completes circuit, conducts e- from signal source through solution to the working electrode
Supporting electrolyte: excess of nonreactive electrolyte (alkali metal) to conduct current
B.) Theory of Voltammetry
1.) Excitation Source: potential set by instrument (working electrode)
- establishes concentration of Reduced and Oxidized Species at electrode based on Nernst Equation:
- reaction at the surface of the electrode
Analyte selectivity is provided by the applied potential on the working electrode.
Electroactive species in the sample solution are drawn towards the working electrode where a half-cell redox reaction takes place.
Another corresponding half-cell redox reaction will also take place at the counter electrode to complete the electron flow.
The resultant current flowing through the electrochemical cell reflects the activity (i.e. concentration) of the electroactive species involved
2.) Current generated at electrode by this process is proportional to concentration at
surface, which in turn is equal to the bulk concentration
For a planar electrode:
measured current (i) = nFADA( )
where:
n = number of electrons in ½ cell reaction
F = Faraday’s constant
A = electrode area (cm2)
D = diffusion coefficient (cm2/s) of A (oxidant)
= slope of curve between CMox,bulk and CMox,s
alternative current best notes to revise on which gives a brief anaylsis of the chapter on the last ituation when you dont have time . i had prepared this presentation for you guys to get good marks in the subject like physics in which the students fears the most . all the best for your boards exam .
Close Loop V/F Control of Voltage Source Inverter using Sinusoidal PWM, Third...IAES-IJPEDS
The aim of this paper to presents a comparative analysis of Voltage Source
Inverter using Sinusoidal Pulse Width Modulation Method, Third Harmonic
Injection Pulse Width Modulation Method and Space Vector Pulse Width
Modulation Two level inverter for Induction Motor. In this paper we have
designed the Simulink model of Inverter for different technique. An above
technique is used to reduce the Total Harmonic Distortion (THD) on the AC
side of the Inverter. The Simulink model is close loop. Results are analyzed
using Fast Fourier Transformation (FFT) which is for analysis of the Total
Harmonic Distortion. All simulations are performed in the MATLAB
Simulink / Simulink environment of MATLAB.
Threshold voltage model for hetero-gate-dielectric tunneling field effect tra...IJECEIAES
In this paper, a two dimensional analytical model of the threshold voltage for HGD TFET structure has been proposed. We have also presented the analytical models for the tunneling width and the channel potential. The potential model is used to develop the physics based model of threshold voltage by exploring the transition between linear to exponential dependence of drain current on the gate bias. The proposed model depends on the drain voltage, gate dielectric near the source and drain, silicon film thickness, work function of gate metal and oxide thickness. The accuracy of the proposed model is verified by simulation results of 2-D ATLAS simulator. Due to the reduction of the equivalent oxide thickness, the coupling between the gate and the channel junction enhances which results in lower threshold voltage. Tunneling width becomes narrower at a given gate voltage for the optimum channel concentration of 10 16 /cm 3 . The higher concentration in the source (N s ) causes a steep bending in the conduction and valence bands compared to the lower concentration which results in smaller tunneling width at the source-channel interface.
A Plasma Tweeter is an audio device which uses a pair of electrodes as a source of sound. It has a clear reproduction and Omni directional radiation pattern. A plasma tweeter has a better frequency response than a conventional speaker and does not involve any moving part (diaphragm) and thus has less reverberation and no wear and tear. Plasma tweeters invented earlier were very expensive. This paper presents a plasma audio system which is making the regular audio system more efficient because of the use of the latest plasma tweeter. Here the objective is to create a low cost and more efficient version of the most speakers invented till now with the complete audio system.
A.) Comparison of Voltammetry to Other Electrochemical Methods
1.) Voltammetry: electrochemical method in which information about an analyte is
obtained by measuring current (i) as a function of applied potential
- only a small amount of sample (analyte) is used
Instrumentation – Three electrodes in solution containing analyte
Working electrode: microelectrode whose potential is varied with time
Reference electrode: potential remains constant (Ag/AgCl electrode or calomel)
Counter electrode: Hg or Pt that completes circuit, conducts e- from signal source through solution to the working electrode
Supporting electrolyte: excess of nonreactive electrolyte (alkali metal) to conduct current
B.) Theory of Voltammetry
1.) Excitation Source: potential set by instrument (working electrode)
- establishes concentration of Reduced and Oxidized Species at electrode based on Nernst Equation:
- reaction at the surface of the electrode
Analyte selectivity is provided by the applied potential on the working electrode.
Electroactive species in the sample solution are drawn towards the working electrode where a half-cell redox reaction takes place.
Another corresponding half-cell redox reaction will also take place at the counter electrode to complete the electron flow.
The resultant current flowing through the electrochemical cell reflects the activity (i.e. concentration) of the electroactive species involved
2.) Current generated at electrode by this process is proportional to concentration at
surface, which in turn is equal to the bulk concentration
For a planar electrode:
measured current (i) = nFADA( )
where:
n = number of electrons in ½ cell reaction
F = Faraday’s constant
A = electrode area (cm2)
D = diffusion coefficient (cm2/s) of A (oxidant)
= slope of curve between CMox,bulk and CMox,s
alternative current best notes to revise on which gives a brief anaylsis of the chapter on the last ituation when you dont have time . i had prepared this presentation for you guys to get good marks in the subject like physics in which the students fears the most . all the best for your boards exam .
Close Loop V/F Control of Voltage Source Inverter using Sinusoidal PWM, Third...IAES-IJPEDS
The aim of this paper to presents a comparative analysis of Voltage Source
Inverter using Sinusoidal Pulse Width Modulation Method, Third Harmonic
Injection Pulse Width Modulation Method and Space Vector Pulse Width
Modulation Two level inverter for Induction Motor. In this paper we have
designed the Simulink model of Inverter for different technique. An above
technique is used to reduce the Total Harmonic Distortion (THD) on the AC
side of the Inverter. The Simulink model is close loop. Results are analyzed
using Fast Fourier Transformation (FFT) which is for analysis of the Total
Harmonic Distortion. All simulations are performed in the MATLAB
Simulink / Simulink environment of MATLAB.
Similar to Tunnel_FET_-_Learning_Module_Draft.pptx (20)
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
10. Relevant Functions (analytical)
SS=
𝜕𝑉𝑔𝑠
𝜕log(𝐼𝑑)
= 𝐥𝐧 𝟏𝟎 ∗ (
𝝏𝑰𝒅
𝝏𝑽𝒈𝒔
∗
𝟏
𝑰𝒅,𝒐𝒏
)−𝟏
𝝏𝑰𝒅
𝝏𝑽𝒈𝒔
= 𝒆
𝝏𝑰𝒅
𝝏𝑬𝒗
𝒄𝒉 =
𝟐𝒆𝟐
𝒉
(
𝝏𝑻𝑾𝑲𝑩
𝑬𝒗
𝒄𝒉 𝑭 𝑬𝒗
𝒄𝒉 + 𝑻𝑾𝑲𝑩
𝝏𝑭(𝑬𝒗
𝒄𝒉)
𝝏𝑬𝒗
𝒄𝒉 )
𝑻𝑾𝑲𝑩 = 𝒆
−
𝟒𝜦 𝟐𝒎∗𝑬𝒈
𝟑
𝟐
𝟑𝒉 ∆𝝓+𝑬𝒈
F 𝑬𝒗
𝒄𝒉 = 𝐸𝑐
𝑠
𝐸𝑣
𝑐ℎ
𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
10
J. Knoch, S. Mantl and J. Appenzeller, "Impact of dimensionality on the performance of tunneling
FETs: Bulk versus one-dimensional devices," ScienceDirect, vol. 51, pp. 572-78, 2007.
11. Literature Review: MOSFET/TFET IV
of different material system
A. M. Ionescu and H. Riel, "Tunnel field-effect transistors as energy-efficient
electronics switches," Nature, vol. 479, pp. 329-337, 2011.
11
12. Literature Review: varying gate
overlap & differential voltage
Gate overlap improves SS
without degrading Ion and Ioff
Differential voltage between top and bottom gate
for a double gate TFET correlates positively with Ion/Ioff
Fiori, G.; Iannaccone, G., "Ultralow-Voltage Bilayer Graphene Tunnel FET," Electron Device Letters,
IEEE , vol.0, no.10, pp.1096,1098, Oct. 2009 doi: 10.1109/LED.2009.2028248
12
13. Literature Review: varying drain-
side gate underlap & drain doping
X. Yang, J. Chauhan, J. Guo, and K. Mohanram “Graphene tunneling FET and its applications in
low-power circuit design,” VLSI, pp. 263-268, 2010
13
Drain-side gate underlap and drain doping reduce the
ambipolar IV characteristics without sacrificing Ion/Ioff and SS
14. Result: varying channel width
14
Channel width varies inversely with
SS and correlates negatively
(exponential) with Ion/Ioff
𝐼𝑑 =
2𝑒
ℎ
𝑊
𝐸𝑐
𝑠
𝐸𝑣
𝑐ℎ
𝑇 𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
15. Result: varying channel width
y = 381.85e-0.554x
R² = 0.9697
y = 3E+08e-2.043x
R² = 0.979
1
10
100
1,000
10,000
100,000
1,000,000
0
50
100
150
200
250
0 1 2 3 4 5 6 7 8
ratio
SS(mV/dec)
width (nm)
SS (mV/dec)
Ion/Ioff
15
Channel width varies inversely with SS and
correlates negatively (exponential) with Ion/Ioff
17. Results varying channel length
17
y = 30782ln(x) - 70513
R² = 0.7531
1
10
100
1,000
10,000
100,000
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Ratio
SS
(mV/dec)
length (nm)
SS (mV/dec)
Ion/Ioff
Channel length varies inversely with SS and
correlates positively (logarithmic) with Ion/Ioff
18. Results: varying doping in contacts
18
Channel doping correlates positively with SS (exponential) and
positively with Ion/Ioff (exponential) up until doping of around 0.28eV
Off
On
𝐸𝑐
𝐸𝑣
q∆𝑉𝐺
λ
Channel
Source Drain
𝑓𝑠 𝐸
19. Results: varying doping in contacts
y = 0.1836e15.587x
R² = 0.8899
y = 20.708e32.662x
R² = 0.9263
y = 3E+07e-33.01x
1
10
100
1,000
10,000
100,000
1,000,000
0
10
20
30
40
50
60
70
0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4
ratio
SS
(mV/dec)
doping (eV)
SS (mV/dec)
Ion/Ioff
19
Channel doping correlates positively with SS (exponential) and
positively with Ion/Ioff (exponential) up until doping of around 0.28eV
20. Results: varying drain bias
20
Drain bias correlates positively with SS (linear & weak)
and negatively with Ion/Ioff (exponential)
Off
On
𝐸𝑐
𝐸𝑣
q∆𝑉𝐺
λ
Channel
Source Drain
𝑓𝑠 𝐸
21. Results: varying drain bias
y = 366373e-26.58x
R² = 0.9464
1
10
100
1,000
10,000
100,000
1,000,000
0
2
4
6
8
10
12
0 0.05 0.1 0.15 0.2 0.25
ratio
SS
(mV/dec)
vd (V)
SS (mV/dec)
Ion/Ioff
21
Drain bias correlates positively with SS (linear & weak)
and negatively with Ion/Ioff (exponential)
22. Conclusion
SS of 6.4 mV/dec and Ion/Ioff of >25,000 were
obtained for length=40nm, width=5nm, vd=0.1 V, and
doping=0.24eV.
Further analysis is required to balance the trade-offs
among size, power, and performance.
In comparison to a MOSFET, high Ion/Ioff ratio and
steep SS over several decades indicate GNR TFET’s
superiority for ultra-low-voltage applications.
22
23. Future direction
Link experimental results with analytical equations
Adjust simulation to account for experimental
challenges
Include scattering (inelastic & elastic)
Alternative TFET designs
23
24. Appendix: Simulation Design
(continue)
Tight-binding Hamiltonian model
TFET setup:
Channel doping
Tri-gate
Non-equilibrium green function (NEGF)
Assumptions:
Room temperature
ballistic transport
electrodes are infinite electron reservoir
steady state
24
25. 𝐼𝑑 =
2𝑒
ℎ
𝑊 𝐸𝑐
𝑠
𝐸𝑣
𝑐ℎ
𝑇 𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
𝐺 = (𝐸𝐼 − 𝐻 − Σ 1 − Σ 2) −1
E : energy matrices from the electronic band structure
H : hamiltonian matrix
Σ 1,2 : self energy matrices from the contacts
Σ 1=Γ1𝑓1 , Σ 2=Γ2𝑓2
Γ: broadening matrices due to coupling with contacts
f: fermi functions describing number of electrons
𝐺𝑛 = 𝐺 Γ1𝑓1 + Γ2𝑓2 𝐺+
Electron density per unit energy
Appendix: NEGF
25
26. Appendix: NEGF (continue)
T(E)=Trace(Γ1𝐺Γ2𝐺+
)
Average transmission at different energy
U=𝑈𝐿 + 𝑈𝑁
Potential energy effecting the DOS , and hence the transmission T
𝑈𝐿 =
𝐶𝐺
𝐶𝐸
(−𝑞𝑉𝐺)+
𝐶𝐷
𝐶𝐸
(−q𝑉𝐷)
𝑈𝑁 =
𝑞2
𝐶𝑒
∆N
𝑓(𝐸) =
1
1+𝑒
𝐸−µ
𝑘𝑇
Probability that an electron will be at an energy state E given the
fermi level µ, and temperature T
𝐼𝑑 =
2𝑒
ℎ
𝑊 𝐸𝑐
𝑠
𝐸𝑣
𝑐ℎ
𝑇 𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
26