IMPACT OF WORK FUNCTION ON ELECTRICAL PERFORMANCE OF NOVEL SI1-XGEX/GAAS JUNCTIONLESS TFET

Abstract

ABSTRACT The present invention provides a system and method to analyze how diverse gate materials with varying work functions can modulate the gate's control over the channel, influencing tunneling efficiency and overall device performance. The analytical framework is expected to identify the optimal work function range for achieving a superior ION/IOFF ratio, a steeper SS, and a higher gm in Si1-xGex/GaAs junctionless T-FETs.

Specification

Description:FORM 2
THE PATENTS ACT, 1970
(39 OF 1970)
&
THE PATENTS RULES, 2003
COMPLETE SPECIFICATION
(See section 10; rule 13)



Title: Impact of Work Function on Electrical Performance of Novel Si1-xGex/GaAs Junctionless TFET




APPLICANT DETAILS:
(a) NAME: GRAPHIC ERA DEEMED TO BE UNIVERSITY
(b) NATIONALITY: Indian
(c) ADDRESS: 566/6, Bell Road, Society Area, Clement Town, Dehradun - 248002,
Uttarakhand, India







PREAMBLE TO THE DESCRIPTION:
The following specification particularly describes the nature of this invention and the manner in which it is to be performed.

Impact of Work Function on Electrical Performance of Novel Si1-xGex/GaAs Junctionless TFET

Field of Invention:
The present invention investigates the enhancement of electrical performance in novel Si1-xGex/GaAs junctionless tunnel field-effect transistors (T-FETs) achieved through controlled variation of the CG work function.

Background of the Invention.
The following background discussion includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication expressly or implicitly referenced is prior art.
The pursuit of reducing the size of semiconductor devices while enhancing their performance has prompted extensive research into novel transistor topologies. TFET has emerged as a viable substitues owing to its potential to outperform conventional devices in terms of scalability, lower leakage current, and greater electrostatic control. The Si1-xGex/GaAs heterostructure integration holds significant promise for high-performance T-FETs due to the exceptional properties of these materials. This study presents an analytical investigation aimed at enhancing the electrical performance of a new Si1-xGex/GaAs junctionless T-FET through strategic modulation of its work function. The absence of a conventional pn junction in the junctionless T-FET architecture offers advantages such as a simplified fabrication process and improved electrostatic control. This research underscores the importance of exploring innovative transistor topologies to further the development of semiconductor devices. We can improve the performance of Si1-xGex/GaAs junctionless T-FETs for next-generation.
The electronics by adjusting the device's parameters. One way to do this is by varying CG work function at the source and drain contacts. Our goal is to investigate how this work function variation affects important performance metrics such as transconductance, on-state current, VT, and SS, Band Energy, Electric field, non-local BTBT electron Tunneling Rate, Total Current Density, Conduction Current Density and parasitic capacitances (Cgs, Cgd, Cgg). We will use systematic analysis and simulation to gain a deeper understanding of these metrics and clarify the working principles behind the performance gains achieved through work function engineering. This study contributes to the growing body of research on advanced transistor design and optimization techniques. These techniques have a broad impact on energy-efficient computing, high-frequency circuits, and low-power electronics.
The present invention expand understanding of Si1-xGex/GaAs junctionless T-FETs and suggest new avenues for future developments in semiconductor device technology.
Object(s) of the present invention:
The primary objective of the present invention is to overcome the drawback associated with prior art.
An object of the present invention is to provide analytical approach to understand the interplay between work function engineering and the Si1-xGex/GaAs material system.

Summary of the Invention:
In an embodiment, the present invention provides a system and method to analyze how diverse gate materials with varying work functions can modulate the gate's control over the channel, influencing tunneling efficiency and overall device performance. The analytical framework is expected to identify the optimal work function range for achieving a superior ION/IOFF ratio, a steeper SS, and a higher gm in Si1-xGex/GaAs junctionless T-FETs.

Brief description of Drawings:
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, explain the disclosed principles. The reference numbers are used throughout the figures to describe the features and components. Some embodiments of system and/or methods in accordance with embodiments of the present subject matter are now described, by way of example only, and regarding the accompanying figures, in which
Figure 1: illustrates structural Design of DD-HJLTFET.
Figure 2: illustrates Id ~ Vgs plot for work function.
Figure 3: illustrates Cgs plot for different Work function.
Figure 4: illustrates Cgd plot for different work functions.
Figure 5: illustrates Cgg plot for different work functions.
.
Figure 6: illustrates Electric field plot for different work functions.
Figure 7: illustrates Band Energy plot for different Work function.
Figure 8: illustrates Non-local BTBT electron tunneling rate plot for
different work function.
Figure 9: illustrates Total current density plot for different work function.
Figure 10: illustrates Conduction current density work function.
Detailed description of the invention:
In the present document, the word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or implementation of the present subject matter described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.
While the disclosure is susceptible to various modifications and alternative forms, specific embodiment thereof has been shown by way of example, in the drawings and will be described in detail below. It should be understood, however, that it is not intended to limit the disclosure to the specific forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the spirit and the scope of the disclosure.
The terms "comprises", "comprising", "includes", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a setup, device or method that comprises a list of components or steps does not include only those components or steps but may include other components or steps not expressly listed or inherent to such setup or device or method. In other words, one or more elements in a system or apparatus proceeded by "comprises... a" does not, without more constraints, preclude the existence of other elements or additional elements in the system or method.
In an embodiment, the present invention provides Si1-xGex/GaAs-JLTFET device's 2-D structure is illustrated in figure 1. The device uses band gap engineering to apply a low band gap composite Si1-xGex/GaAs at the source area and a high band gap composite GaAs at the drain
and channel area. HfO2 and SiO2 are used at both gates in the same thickness to prevent leakage current. A 2 nm gap is made between the polar gate and control gate to isolate them. The parameter's details are shown in Table. I

Si1-xGex/GaAs Junctionless TFET
Property Dimension Units
LSE /LCL / LDN 20 nm
TCG /TPG Thickness 2 nm
TH /TS Thickness 1 nm
LPG Work Function 5.93 eV
LCG Work Function 3.5/ 3.7/ 4.54 eV
Si1-xGex/GaAs Material Thickness 3 nm
Spacer Thickness 2 nm
LSP 2 nm


The Silvaco TCAD simulator is utilized to simulate the apparatus under examination, while the rate of recombination tunneling is estimated using the BTBT model. The internal physical operations of the device are taken into consideration by the TCAD model. The channel/drain border is defined to permit both forward and reverse tunneling, while the source/channel is regarded as a quantum tunneling zone. Auger recombination and the Shockley-Read-Hall models are employed to explain the carrier recombination process, while the off-state is dominated by the trap-assisted tunneling paradigm. The Wentzel-Kramers-Brillouin approach is used to quantitatively estimate the tunneling probability, and Hansch's quantum confinement model is employed to enhance the simulation's precision. The carrier transport equations are numerically solved in simulations using techniques developed by Gummel and Newton.
Figure 2 illustrates the interrelation between drain current (Id) and gate voltage (Vgs) in a Tunnel Field-Effect Transistor (TFET) across three distinct work function values: 4.54 eV, 3.7 eV, and 3.5 eV. Drain current is measured in amperes (A) while gate voltage is expressed in volts (V). A key component of this research is the work function, which represents the minimal energy needed to release an electron from a material's surface. In TFET operation, the gate voltage assumes control over the channel's conductivity, governing the flow of charge carriers between the source and drain terminals. Upon application of a voltage to the gate, an electric field arises, either attracting or repelling charge carriers within the channel, contingent upon the TFET type. This phenomenon directly influences the magnitude of current traversing through the drain.

Figure 3 represents the gate capacitance (Cgs) and gate voltage. The gate capacitance (Cgs) plays a pivotal role in determining their operational behavior. Cgs denotes the capacitance associated with the gate terminal, representing the ability of the transistor to store electric charge per unit of applied voltage. As the Vgs modulates, it governs the conductivity of the channel between the source and drain terminals, thereby exerting control over the transistor's performance. From Figure 3, it can be analyzed that as the Vgs rise, the gate capacitance (Cgs) of the TFET exhibits a corresponding rise. This observed behavior is crucial for understanding the device's electrical characteristics and informs design considerations for various electronic applications.
Figure 4 demonstrates the correlation between Cgd and Vgs in a TFET. Here, Gate capacitance represents a critical parameter in TFET operation, signifying the charge required for voltage modulation at the gate terminal and it is measure in femtofarads per micrometer (fF/µm). Cgd signifies the capacitance between the gate and the drain of the transistor, Cgs refers to the capacitance between the gate and the source. However, the y-axis labels of the graph erroneously denote "Work Function (eV)" instead of the accurate specification, "Cgd (10-18 F/µm)". It's essential to discern between Cgd and Cgs within TFETs. The figure illustrates a slight increment in Cgd with escalating gate Vgs. This observation can be imputed to the narrowing of the depletion region between the drain and the channel as the gate voltage rises. Consequently, this reduction in depletion region width augments the overlap between the gate and the drain, thereby elevating capacitance.
Figure 5 depicts the interaction between Cgg and Vgs in a TFET. Gate capacitance is quantified in femtofarads per micrometer (F/µm), while gate voltage is expressed in volts (V). Gate capacitance (Cgg) stands as a pivotal parameter, delineating the quantity of charge requisite to modulate the voltage at the gate terminal. From the figure, it can be noted that the y-axis labels are erroneously labeled as "Work Function (eV)" instead of the accurate designation, " Cgg (10-18 F/µm)". A discernible trend can be seen in the graph wherein gate capacitance increases concomitantly with escalating gate voltage. This phenomenon finds its rational in the accumulation of majority charge carriers within the channel, instigated by the applied gate voltage.
Figure 6 demonstrates the spatial distribution of electrical field intensity emitted by a device across varying distances. The X-axis denotes "Distance (nm)" while the Y-axis represents "Electric field (105 V/cm)". Notably, the absence of a legend complicates the identification of the two lines, which presumably signify the maximum electrical field intensity at specific distances. From the figure,it can be observed that the electric field intensity peaks at a distance of 0 nm, diminishing progressively as distance increases. This spatial decay hints at the likelihood of a localized source generating the electric field, positioned at the origin (0 nm) on the X-axis. The rapid attenuation of electric field intensity over short distances, suggests intricate interactions between the material properties traversed by the electric field and the geometric characteristics of its source. This phenomenon underscores the importance of elucidating the underlying factors influencing electric field propagation, be it material composition or source geometry. Further analysis and interpretation, aided by a comprehensive legend, are imperative for a nuanced understanding of the depicted electrical field distribution.
Figure 7 represents the variation of work function considering distance between two objects. X- axis represents "Distance" in "nm" and Y- axis represents "Work Function" in "eV". Work Function is the minimum energy that is required to release an electron from a material's surface. Two distinct lines have been used in the figure to show the work function at particular distances for two different materials. Identification of the materials presented becomes difficult due to the absence of a legend. The lines can be distinguished on the basis of their characteristics which represent distinct work functions of their respective materials. It is a major step to understand the interplay of work function and distance between materials.
Figure 8 demonstrates the relationship between non-local electron transfer rate and distance within a device. X- axis represents "Distance" in "nm" and Y- axis represents "Non-Local BTBT e Rate" in "/cm³s". "BTBT" is basically related to "hole-to-hole" charge transfer, where a hole i.e. absence of an electron migrates from one molecular site to another. Particularly the "non-local" electron transfer implies to examples where an electron migrates between molecules over commensurate vast distances. It can be noted that the rate depicted on the y-axis is expressed per cubic centimeter of the material, signifying the frequency of the process within a unit volume. It is crucial to recognize that the rate of non-local electron transfer is generally markedly slower compared to local electron transfer, wherein electrons migrate between adjacent molecules. The absence of a legend accompanying the graph precludes identification of the three distinct materials plotted. However, the delineation of the lines by color suggests differentiation among materials, each potentially exhibiting unique characteristics influencing non-local electron transfer.
Figure 9 illustrates the current density characteristics of a transistor plotted against distance. The X-axis is labeled "Distance (nm)" while the Y-axis denotes "Total Current Density (106 A/cm²)". Notably, the y-axis labels mistakenly indicate "Work Function (eV)" instead of the precise descripton, "Current Density (106 A/cm²)". This figure incorporates three distinct work functions (4.54 eV, 3.7 eV, and 3.5 eV), as indicated by the legend. Work function is the least energy required to free an electron from a material's surface, and it is a crucial metric in semiconductor physics. In the context of a TFET, the Vgs administration governs the channel's conductivity between the source and drain terminals. Application of voltage to the gate engenders an electric field, manipulating the motion of charge carriers within the channel, contingent upon TFET type. Consequently, this modulation profoundly influences the magnitude of current flowing through the drain terminal.
Figure 10 illustrates the fluctuation of conduction current density concerning distance within a conductor. The X-axis denotes "Distance (nm)" while the Y-axis represents "Conduction Current Density (106 A/cm²)". From the figure it can be that the y-axis labels erroneously indicate "Work Function (eV)" instead of the accurate descriptor, "Current Density (106 A/cm²)". Conduction current density serves as a metric quantifying the magnitude of electric current flowing through a unit area of the conductor. Figure illustrates a characteristic where current density is notably concentrated at the conductor's surface, displaying an exponential decay as distance from the surface increases. This observed phenomenon suggests a distribution wherein current flows predominantly near the surface, gradually diminishing in magnitude as distance from the surface increases. This behavior aligns with the typical surface conduction properties exhibited by certain conductors.

TABLE II. VARIATION OF PARAMETER BASED ON WORK FUNCTION
S.No. Work Function(eV) SS (mV/ dec) gm(µS) ION (A/µm) IOFF
(A/µm)
1. 3.5 0.1684 0.00079 0.00062 1.871
2. 3.7 0.122 0.00079 0.00058 3.699
3. 4.54 0.037 0.00025 5.200 1.202



In an embodiment, the work function can greatly improve the electrical performance of a unique Si1-xGex/GaAs junctionless TFET device. Its performance is influenced by various factors, including transconductance, subthreshold swing, on-current, and off-current. In order to achieve maximum performance, it's important to minimize parasitic capacitances that might impact the device's operation. The electric field and band energy should also be considered. To replace traditional MOSFET devices, it's necessary to maximize these properties to achieve a high on-state current density and a low subthreshold swing. The work function has a major impact on the band alignment and tunneling probability of the device. It's crucial to take into account the impact of work function effects on the electron tunneling rate of BTBT Improving the work function can increase the tunneling rate and enhance a device's performance. Additionally, the electrical performance of Si1-xGex/GaAs junctionless TFETs is significantly impacted by the device's geometry and structure. A well-designed device structure can reduce parasitic effects and improve the overall performance of the device. Therefore, it is crucial to thoroughly evaluate these factors to ensure improved gadget performance and efficiency.
, Claims:FORM 2
THE PATENTS ACT, 1970
(39 OF 1970)
&
THE PATENTS RULES, 2003
COMPLETE SPECIFICATION
(See section 10; rule 13)



Title: Impact of Work Function on Electrical Performance of Novel Si1-xGex/GaAs Junctionless TFET




APPLICANT DETAILS:
(a) NAME: GRAPHIC ERA DEEMED TO BE UNIVERSITY
(b) NATIONALITY: Indian
(c) ADDRESS: 566/6, Bell Road, Society Area, Clement Town, Dehradun - 248002,
Uttarakhand, India







PREAMBLE TO THE DESCRIPTION:
The following specification particularly describes the nature of this invention and the manner in which it is to be performed.

Impact of Work Function on Electrical Performance of Novel Si1-xGex/GaAs Junctionless TFET

Field of Invention:
The present invention investigates the enhancement of electrical performance in novel Si1-xGex/GaAs junctionless tunnel field-effect transistors (T-FETs) achieved through controlled variation of the CG work function.

Background of the Invention.
The following background discussion includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication expressly or implicitly referenced is prior art.
The pursuit of reducing the size of semiconductor devices while enhancing their performance has prompted extensive research into novel transistor topologies. TFET has emerged as a viable substitues owing to its potential to outperform conventional devices in terms of scalability, lower leakage current, and greater electrostatic control. The Si1-xGex/GaAs heterostructure integration holds significant promise for high-performance T-FETs due to the exceptional properties of these materials. This study presents an analytical investigation aimed at enhancing the electrical performance of a new Si1-xGex/GaAs junctionless T-FET through strategic modulation of its work function. The absence of a conventional pn junction in the junctionless T-FET architecture offers advantages such as a simplified fabrication process and improved electrostatic control. This research underscores the importance of exploring innovative transistor topologies to further the development of semiconductor devices. We can improve the performance of Si1-xGex/GaAs junctionless T-FETs for next-generation.
The electronics by adjusting the device's parameters. One way to do this is by varying CG work function at the source and drain contacts. Our goal is to investigate how this work function variation affects important performance metrics such as transconductance, on-state current, VT, and SS, Band Energy, Electric field, non-local BTBT electron Tunneling Rate, Total Current Density, Conduction Current Density and parasitic capacitances (Cgs, Cgd, Cgg). We will use systematic analysis and simulation to gain a deeper understanding of these metrics and clarify the working principles behind the performance gains achieved through work function engineering. This study contributes to the growing body of research on advanced transistor design and optimization techniques. These techniques have a broad impact on energy-efficient computing, high-frequency circuits, and low-power electronics.
The present invention expand understanding of Si1-xGex/GaAs junctionless T-FETs and suggest new avenues for future developments in semiconductor device technology.
Object(s) of the present invention:
The primary objective of the present invention is to overcome the drawback associated with prior art.
An object of the present invention is to provide analytical approach to understand the interplay between work function engineering and the Si1-xGex/GaAs material system.

Summary of the Invention:
In an embodiment, the present invention provides a system and method to analyze how diverse gate materials with varying work functions can modulate the gate's control over the channel, influencing tunneling efficiency and overall device performance. The analytical framework is expected to identify the optimal work function range for achieving a superior ION/IOFF ratio, a steeper SS, and a higher gm in Si1-xGex/GaAs junctionless T-FETs.

Brief description of Drawings:
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, explain the disclosed principles. The reference numbers are used throughout the figures to describe the features and components. Some embodiments of system and/or methods in accordance with embodiments of the present subject matter are now described, by way of example only, and regarding the accompanying figures, in which
Figure 1: illustrates structural Design of DD-HJLTFET.
Figure 2: illustrates Id ~ Vgs plot for work function.
Figure 3: illustrates Cgs plot for different Work function.
Figure 4: illustrates Cgd plot for different work functions.
Figure 5: illustrates Cgg plot for different work functions.
.
Figure 6: illustrates Electric field plot for different work functions.
Figure 7: illustrates Band Energy plot for different Work function.
Figure 8: illustrates Non-local BTBT electron tunneling rate plot for
different work function.
Figure 9: illustrates Total current density plot for different work function.
Figure 10: illustrates Conduction current density work function.
Detailed description of the invention:
In the present document, the word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or implementation of the present subject matter described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.
While the disclosure is susceptible to various modifications and alternative forms, specific embodiment thereof has been shown by way of example, in the drawings and will be described in detail below. It should be understood, however, that it is not intended to limit the disclosure to the specific forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the spirit and the scope of the disclosure.
The terms "comprises", "comprising", "includes", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a setup, device or method that comprises a list of components or steps does not include only those components or steps but may include other components or steps not expressly listed or inherent to such setup or device or method. In other words, one or more elements in a system or apparatus proceeded by "comprises... a" does not, without more constraints, preclude the existence of other elements or additional elements in the system or method.
In an embodiment, the present invention provides Si1-xGex/GaAs-JLTFET device's 2-D structure is illustrated in figure 1. The device uses band gap engineering to apply a low band gap composite Si1-xGex/GaAs at the source area and a high band gap composite GaAs at the drain
and channel area. HfO2 and SiO2 are used at both gates in the same thickness to prevent leakage current. A 2 nm gap is made between the polar gate and control gate to isolate them. The parameter's details are shown in Table. I

Si1-xGex/GaAs Junctionless TFET
Property Dimension Units
LSE /LCL / LDN 20 nm
TCG /TPG Thickness 2 nm
TH /TS Thickness 1 nm
LPG Work Function 5.93 eV
LCG Work Function 3.5/ 3.7/ 4.54 eV
Si1-xGex/GaAs Material Thickness 3 nm
Spacer Thickness 2 nm
LSP 2 nm


The Silvaco TCAD simulator is utilized to simulate the apparatus under examination, while the rate of recombination tunneling is estimated using the BTBT model. The internal physical operations of the device are taken into consideration by the TCAD model. The channel/drain border is defined to permit both forward and reverse tunneling, while the source/channel is regarded as a quantum tunneling zone. Auger recombination and the Shockley-Read-Hall models are employed to explain the carrier recombination process, while the off-state is dominated by the trap-assisted tunneling paradigm. The Wentzel-Kramers-Brillouin approach is used to quantitatively estimate the tunneling probability, and Hansch's quantum confinement model is employed to enhance the simulation's precision. The carrier transport equations are numerically solved in simulations using techniques developed by Gummel and Newton.
Figure 2 illustrates the interrelation between drain current (Id) and gate voltage (Vgs) in a Tunnel Field-Effect Transistor (TFET) across three distinct work function values: 4.54 eV, 3.7 eV, and 3.5 eV. Drain current is measured in amperes (A) while gate voltage is expressed in volts (V). A key component of this research is the work function, which represents the minimal energy needed to release an electron from a material's surface. In TFET operation, the gate voltage assumes control over the channel's conductivity, governing the flow of charge carriers between the source and drain terminals. Upon application of a voltage to the gate, an electric field arises, either attracting or repelling charge carriers within the channel, contingent upon the TFET type. This phenomenon directly influences the magnitude of current traversing through the drain.

Figure 3 represents the gate capacitance (Cgs) and gate voltage. The gate capacitance (Cgs) plays a pivotal role in determining their operational behavior. Cgs denotes the capacitance associated with the gate terminal, representing the ability of the transistor to store electric charge per unit of applied voltage. As the Vgs modulates, it governs the conductivity of the channel between the source and drain terminals, thereby exerting control over the transistor's performance. From Figure 3, it can be analyzed that as the Vgs rise, the gate capacitance (Cgs) of the TFET exhibits a corresponding rise. This observed behavior is crucial for understanding the device's electrical characteristics and informs design considerations for various electronic applications.
Figure 4 demonstrates the correlation between Cgd and Vgs in a TFET. Here, Gate capacitance represents a critical parameter in TFET operation, signifying the charge required for voltage modulation at the gate terminal and it is measure in femtofarads per micrometer (fF/µm). Cgd signifies the capacitance between the gate and the drain of the transistor, Cgs refers to the capacitance between the gate and the source. However, the y-axis labels of the graph erroneously denote "Work Function (eV)" instead of the accurate specification, "Cgd (10-18 F/µm)". It's essential to discern between Cgd and Cgs within TFETs. The figure illustrates a slight increment in Cgd with escalating gate Vgs. This observation can be imputed to the narrowing of the depletion region between the drain and the channel as the gate voltage rises. Consequently, this reduction in depletion region width augments the overlap between the gate and the drain, thereby elevating capacitance.
Figure 5 depicts the interaction between Cgg and Vgs in a TFET. Gate capacitance is quantified in femtofarads per micrometer (F/µm), while gate voltage is expressed in volts (V). Gate capacitance (Cgg) stands as a pivotal parameter, delineating the quantity of charge requisite to modulate the voltage at the gate terminal. From the figure, it can be noted that the y-axis labels are erroneously labeled as "Work Function (eV)" instead of the accurate designation, " Cgg (10-18 F/µm)". A discernible trend can be seen in the graph wherein gate capacitance increases concomitantly with escalating gate voltage. This phenomenon finds its rational in the accumulation of majority charge carriers within the channel, instigated by the applied gate voltage.
Figure 6 demonstrates the spatial distribution of electrical field intensity emitted by a device across varying distances. The X-axis denotes "Distance (nm)" while the Y-axis represents "Electric field (105 V/cm)". Notably, the absence of a legend complicates the identification of the two lines, which presumably signify the maximum electrical field intensity at specific distances. From the figure,it can be observed that the electric field intensity peaks at a distance of 0 nm, diminishing progressively as distance increases. This spatial decay hints at the likelihood of a localized source generating the electric field, positioned at the origin (0 nm) on the X-axis. The rapid attenuation of electric field intensity over short distances, suggests intricate interactions between the material properties traversed by the electric field and the geometric characteristics of its source. This phenomenon underscores the importance of elucidating the underlying factors influencing electric field propagation, be it material composition or source geometry. Further analysis and interpretation, aided by a comprehensive legend, are imperative for a nuanced understanding of the depicted electrical field distribution.
Figure 7 represents the variation of work function considering distance between two objects. X- axis represents "Distance" in "nm" and Y- axis represents "Work Function" in "eV". Work Function is the minimum energy that is required to release an electron from a material's surface. Two distinct lines have been used in the figure to show the work function at particular distances for two different materials. Identification of the materials presented becomes difficult due to the absence of a legend. The lines can be distinguished on the basis of their characteristics which represent distinct work functions of their respective materials. It is a major step to understand the interplay of work function and distance between materials.
Figure 8 demonstrates the relationship between non-local electron transfer rate and distance within a device. X- axis represents "Distance" in "nm" and Y- axis represents "Non-Local BTBT e Rate" in "/cm³s". "BTBT" is basically related to "hole-to-hole" charge transfer, where a hole i.e. absence of an electron migrates from one molecular site to another. Particularly the "non-local" electron transfer implies to examples where an electron migrates between molecules over commensurate vast distances. It can be noted that the rate depicted on the y-axis is expressed per cubic centimeter of the material, signifying the frequency of the process within a unit volume. It is crucial to recognize that the rate of non-local electron transfer is generally markedly slower compared to local electron transfer, wherein electrons migrate between adjacent molecules. The absence of a legend accompanying the graph precludes identification of the three distinct materials plotted. However, the delineation of the lines by color suggests differentiation among materials, each potentially exhibiting unique characteristics influencing non-local electron transfer.
Figure 9 illustrates the current density characteristics of a transistor plotted against distance. The X-axis is labeled "Distance (nm)" while the Y-axis denotes "Total Current Density (106 A/cm²)". Notably, the y-axis labels mistakenly indicate "Work Function (eV)" instead of the precise descripton, "Current Density (106 A/cm²)". This figure incorporates three distinct work functions (4.54 eV, 3.7 eV, and 3.5 eV), as indicated by the legend. Work function is the least energy required to free an electron from a material's surface, and it is a crucial metric in semiconductor physics. In the context of a TFET, the Vgs administration governs the channel's conductivity between the source and drain terminals. Application of voltage to the gate engenders an electric field, manipulating the motion of charge carriers within the channel, contingent upon TFET type. Consequently, this modulation profoundly influences the magnitude of current flowing through the drain terminal.
Figure 10 illustrates the fluctuation of conduction current density concerning distance within a conductor. The X-axis denotes "Distance (nm)" while the Y-axis represents "Conduction Current Density (106 A/cm²)". From the figure it can be that the y-axis labels erroneously indicate "Work Function (eV)" instead of the accurate descriptor, "Current Density (106 A/cm²)". Conduction current density serves as a metric quantifying the magnitude of electric current flowing through a unit area of the conductor. Figure illustrates a characteristic where current density is notably concentrated at the conductor's surface, displaying an exponential decay as distance from the surface increases. This observed phenomenon suggests a distribution wherein current flows predominantly near the surface, gradually diminishing in magnitude as distance from the surface increases. This behavior aligns with the typical surface conduction properties exhibited by certain conductors.

TABLE II. VARIATION OF PARAMETER BASED ON WORK FUNCTION
S.No. Work Function(eV) SS (mV/ dec) gm(µS) ION (A/µm) IOFF
(A/µm)
1. 3.5 0.1684 0.00079 0.00062 1.871
2. 3.7 0.122 0.00079 0.00058 3.699
3. 4.54 0.037 0.00025 5.200 1.202



In an embodiment, the work function can greatly improve the electrical performance of a unique Si1-xGex/GaAs junctionless TFET device. Its performance is influenced by various factors, including transconductance, subthreshold swing, on-current, and off-current. In order to achieve maximum performance, it's important to minimize parasitic capacitances that might impact the device's operation. The electric field and band energy should also be considered. To replace traditional MOSFET devices, it's necessary to maximize these properties to achieve a high on-state current density and a low subthreshold swing. The work function has a major impact on the band alignment and tunneling probability of the device. It's crucial to take into account the impact of work function effects on the electron tunneling rate of BTBT Improving the work function can increase the tunneling rate and enhance a device's performance. Additionally, the electrical performance of Si1-xGex/GaAs junctionless TFETs is significantly impacted by the device's geometry and structure. A well-designed device structure can reduce parasitic effects and improve the overall performance of the device. Therefore, it is crucial to thoroughly evaluate these factors to ensure improved gadget performance and efficiency.

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