DE202022105580U1 - System for developing and analyzing a parameter of a Bohm quantum potential device (BQP) - Google Patents

Abstract

A system (100) for developing and analyzing at least one parameter of a Bohm quantum potential (BQP) device, the BQP device of the system (100) comprising:
a gate (102) of a first material to avoid depletion effects;
a source and a drain contact (104a, 104b), each made of a second material; and
a pair of dielectric layers (106) composed of a third material, the pair of dielectric layers being disposed on either side of the source and drain contacts (104a, 104b), resulting in the formation of a channel.

Description

FIELD OF THE INVENTION

The present invention relates to a field of multi-gate field effect transistors (FinFET). In particular, the present invention relates to a system for analyzing effects of matching parameters in Bohm quantum potential (BQP) devices of double-gate n-FinFET and Y-parameter extraction in the THz range.

BACKGROUND OF THE INVENTION

With today's semiconductor technology, gate lengths have dropped below 20 nm. Therefore, quantum effects become important. The need to reduce transistor size is a perennial problem to be solved in the integrated circuit art. One way to reduce transistor size is to reduce the length of the channel. In this way, the total area of the transistor can be effectively reduced. However, a minimum channel length (relative to other physical parameters of the transistor) was then achieved, leading to problems with short channel effects. Device scaling has reached a limit due to short channel effects (SCEs) and the quantum behavior of charge carriers. Because of the scaling, there is tunneling through the gate insulator, requiring a change in gate control, which is a function of Vgs. Here, quantum confinement leads to a shift in the Vth and thus to a significant increase in the Tox of the devices. At this level, quantum mechanics became more powerful than classical mechanics. Aggressive scaling of gate spacing has forced designs for Intel's 22nm technology to use self-aligned contacts. At the side of the contact, the width and length of the gate spacers fill up the remaining gate spacing. If the width between two gate spacers is reduced, the contact resistance increases exponentially. Therefore, the gate length is reduced. This range limits gate length scalability for planar devices.

Therefore, an alternative device structure is required to improve the controllability of the channels.

Multi-gate FETs (like FinFET) offer better short-channel control and very low in-channel doping requirements; therefore, the transverse field in the channel is lower, which improves the sub-threshold swing (SS) and lowers the threshold voltage, improving device performance. Another important property of a lightly doped channel is the lower scattering of the dopant ions. It provides better drive current and lower fluctuations in random doping.

Various work has been done on dual gate fin FETs in the past.

KR100748261B1 discloses a low leakage current fin field effect transistor and a method of fabricating the fin FET.

US6812119B1 discloses a method of forming fins for a dual gate fin field effect transistor (FinFET) comprising forming a second layer of semiconducting material over a first layer of semiconducting material and forming double caps in the second layer of semiconducting material. The method further includes forming spacers on the sides of each of the double caps and forming double fins in the first layer of semiconductor material beneath the double caps. The process also includes thinning out the twin laminae to produce narrow twin laminae.

US6885055B2 discloses a dual gate FinFET device and method of fabricating same. More particularly, the invention relates to an electrically stable dual-gate FinFET device and method of fabrication in which the active fin region on a silicon substrate in which the device channel and body are to be formed is nanoscale in width with which substrate is bonded and formed in the shape of a wall along the channel longitudinal direction.

In a FinFET, the gate wraps around a thin piece of (preferably undoped) silicon, also known as the "fin", and the drain currents flow with the side and top surfaces of the fin. The gate wrapped around the channel increases electrostatic control over the channel. As a result who reduces the SCEs and leakage currents. The FinFET offers structural parameters such as fin width, fin height and gate length.

Conventional double-gate MOS devices are made with SOI wafers, which are more expensive than silicon wafers. In addition, there are problems such as B. the floating body effect, a larger parasitic source / drain resistance, an increase in quiescent current and a deterioration in heat transfer to the substrate.

However, scaling is required to improve the digital performance of devices according to Moore's Law, but scaling also degrades analog and RF performance in many ways.

Therefore, there is a need to develop a system and analyze the effects of fitting parameters in Bohm quantum potential (BQP) devices.

The technical advance disclosed by the present invention overcomes the limitations and disadvantages of existing and conventional systems and methods.

SUMMARY OF THE INVENTION

• Ein Ziel der vorliegenden Erfindung ist es, einen Parameter der BQP-Vorrichtung zu entwickeln und zu analysieren;
• Ein weiteres Ziel der vorliegenden Erfindung ist die Analyse der Auswirkungen von Anpassungsparametern in einer Bohm-Quantenpotential-Vorrichtung (BQP);
• Ein weiteres Ziel der vorliegenden Erfindung ist die Untersuchung und der Vergleich des Sub-Threshold Swing (SS)-Werts für verschiedene High-k-Gate-Dielektrikum-Materialien in Abhängigkeit vom Anpassungsparameter (a);
• Ein weiteres Ziel der vorliegenden Erfindung ist es, die Leistung des vorgeschlagenen Systems in Abhängigkeit von der physikalischen Gate-Länge des TiO₂-basierten DG n-Fin FET zu analysieren; und
• Ein weiteres Ziel der vorliegenden Erfindung ist es, Elemente des Kleinsignal-Schaltungsmodells zu analysieren, indem der Y-Parameter bei Frequenzen bis zu 2.5 THz verwendet wird.

The present invention relates generally to a system for developing and analyzing a parameter of a Bohm Quantum Potential (BQP) device.

• An object of the present invention is to develop and analyze a parameter of the BQP device;
• Another object of the present invention is to analyze the effects of adjustment parameters in a Bohm Quantum Potential Device (BQP);
• Another objective of the present invention is to study and compare the sub-threshold swing (SS) value for different high-k gate dielectric materials as a function of the matching parameter (a);
• Another aim of the present invention is to analyze the performance of the proposed system depending on the physical gate length of the TiO ₂ -based DG n-Fin FET; and
• Another object of the present invention is to analyze elements of the small-signal circuit model using the Y-parameter at frequencies up to 2.5 THz.

• ein Gate aus einem ersten Material zur Vermeidung von Verarmungseffekten;
• einen Source- und einen Drain-Kontakt, die jeweils aus einem zweiten Material bestehen; und
• ein Paar dielektrischer Schichten, die aus einer dritten Schicht bestehen, wobei das Paar dielektrischer Schichten auf beiden Seiten des Source- und Drainkontakts angeordnet ist, was zur Bildung eines Kanals führt.

In one embodiment, a system for designing and analyzing at least one parameter of a Bohm quantum potential (BQP) device, the system comprising:

• a gate made of a first material to avoid depletion effects;
• a source and a drain contact each made of a second material; and
• a pair of dielectric layers consisting of a third layer, the pair of dielectric layers being arranged on either side of the source and drain contact, resulting in the formation of a channel.

In one embodiment, the first material to form the gate is titanium nitride (TiN) with a work function of 4-5eV.

In one embodiment, the second material for forming the source and drain contacts is an aluminum electrode with an n-doping concentration (10 ¹⁹ cm ^-3 ), while the channel has a lightly doped p-doping (10 ¹⁶ cm ^-3 ).

In one embodiment, gate resistance is analyzed by determining either the Y or Z parameters at high frequency from a small signal non-quasi-static (NQS) device.

In one embodiment, the NQS small signal device consists of an intrinsic and an extrinsic part, where the intrinsic part contains bias dependent elements and the extrinsic part contains bias independent elements.

In one embodiment, a plurality of extrinsic parameters are first calculated by a calculation module to obtain zero-bias gate-source and gate-drain capacitances, where the intrinsic Y parameter is calculated in the strongly inverted region.

In order to further clarify the advantages and features of the present invention, a more detailed description of the invention will be made by reference to specific embodiments thereof illustrated in the accompanying figures. It is understood that these figures show only typical embodiments of the invention and therefore should not be considered as limiting its scope. The invention will be described and illustrated with additional specificity and detail with the accompanying figures.

character list

• 1 ein Blockdiagramm eines Systems zur Entwicklung und Analyse von mindestens einem Parameter eines Bohm-Quanten-Potential-Geräts (BQP) zeigt, und
• 2 zeigt ein schematisches Layout des nicht quasistatischen Kleinsignal-Ersatzschaltbildes von DG n-FinFETs. Y^int gibt die Y -Parameter nach dem De-Embedding von Cgs0, Cgd0, Rs und Rd an.

These and other features, aspects and advantages of the present invention will be better understood when the following detailed description is read with reference to the accompanying figures, in which like characters represent like parts throughout the figures, wherein:

• 1 shows a block diagram of a system for development and analysis of at least one parameter of a Bohm Quantum Potential (BQP) device, and
• 2 shows a schematic layout of the non-quasi-static small-signal equivalent circuit of DG n-FinFETs. Y ^int specifies the Y parameters after de-embedding Cgs0, Cgd0, Rs, and Rd.

Those skilled in the art will understand that the elements in the figures are presented for simplicity and are not necessarily drawn to scale. For example, the flow charts illustrate the method of key steps to enhance understanding of aspects of the present disclosure. In addition, one or more components of the device may be represented in the figures by conventional symbols, and the figures only show the specific details relevant to understanding the embodiments of the present disclosure, not to encircle the figures with details to overload, which are easily recognizable to those skilled in the art familiar with the present description.

DETAILED DESCRIPTION:

For the purposes of promoting an understanding of the invention, reference will now be made to the embodiment illustrated in the figures and specific language will be used to describe the same. It should be understood, however, that no limitation on the scope of the invention is intended, and such alterations and further modifications to the illustrated system and such further applications of the principles of the invention set forth therein are contemplated as would occur to those skilled in the art invention would normally come to mind.

Those skilled in the art will understand that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not to be taken as limiting.

When this specification refers to "an aspect," "another aspect," or the like, it means that a particular feature, structure, or characteristic described in connection with the embodiment is present in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in another embodiment," and similar phrases throughout this specification may or may not all refer to the same embodiment.

The terms "comprises," "including," or other variations thereof are intended to cover non-exclusive inclusion, such that a method or method that includes a list of steps includes not only those steps, but may also include other steps that are not expressly stated or pertaining to any such process or method. Likewise, any device or subsystem or element or structure or component preceded by "comprises...a" does not, without further limitation, exclude the existence of other devices or other subsystem or other element or other structure or other component or additional device or additional subsystems or additional elements or additional structures or additional components.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one skilled in the art to which this invention pertains. The system, methods, and examples provided herein are for purposes of illustration only and are not intended to be limiting.

Embodiments of the present invention are described in detail below with reference to the attached figures.

1 Figure 1 shows a block diagram of a system (100) for developing and analyzing at least one parameter of a Bohm quantum potential (BQP) device, the BQP device of the system (100) comprising: a gate (102), a source and a drain contact (104a, 104b) and a pair of dielectric layer (106).

The gate (102) consists of a first material in order to avoid depletion effects. The first material to form the gate (102) is titanium nitride (TiN) with a work function of 4-5eV.

The source and a drain contact (104a, 104b) each consist of a second material. The second material for forming the source and drain contacts (104a, 104b) is an aluminum electrode with an n-type doping concentration (10 ¹⁹ cm ^-3 ), while the channel has a lightly doped p-type doping concentration (10 ¹⁶ cm ^-3 ).

The pair of dielectric layers (106) is made of a third material, the pair of dielectric layers being disposed on either side of the source and drain contacts (104a, 104b), resulting in the formation of a channel.

Gate resistance is analyzed by determining either the Y or Z parameter at high frequency from a small-signal non-quasi-static (NQS) device. The NQS small-signal device consists of an intrinsic and an extrinsic part, with the intrinsic part containing bias-dependent elements and the extrinsic part containing bias-independent elements. The plurality of extrinsic parameters are initially calculated by a calculation module to obtain gate-source and gate-drain capacitances at zero bias, where the intrinsic Y parameter is calculated in the strong inversion region. Table 1. Parameters of the TiO2 DG n-FinFET parameter Values Gate length (L _g ) 20nm BOX thickness (t _box ) 5nm Height of fin (H _fin ) 10nm Width of fin (W _fin ) 5nm Device layer doping (N _d ) 10 ^{19cm -3} Goal work function 4.65 possibly Gate Oxide Thickness (tox) 1nm

2 shows a schematic layout of the non-quasi-static small-signal equivalent circuit of DG n-FinFETs. Y ^int returns the Y parameters after de-embedding Cgs0, Cgd0, Rs, and Rd.

C _gd0 and C _gs0 denote the extrinsic capacitances from gate to drain and from gate to source, respectively. R _s and R _d are the source and drain resistances, respectively. The distributed channel resistances are Rgs and _Rgd . L _sd is the source-drain inductance. The effect of the time constant in the source-drain admittance (-y _sd ) is taken into account. C _sdx is the capacitance due to the DIBL effect in a short channel FIN FET device.

The exact calculation of the intrinsic parameters of the fin FET is only done after the extrinsic parameters C _gs0 and C _{gd0 have been} removed from the simulated Y parameters. Therefore, the extrinsic parameters are calculated first. For the calculation of the gate-source and gate-drain capacitances at zero bias, the intrinsic part of the circuit is ignored. $$\begin{array}{c}{\text{I}}_1={\text{Y}}_{11}{\text{V}}_1+{\text{Y}}_{12}{\text{V}}_2\\ {\text{I}}_2={\text{Y}}_{12}{\text{V}}_1+{\text{Y}}_{22}{\text{V}}_2\end{array}$$

$$\begin{array}{l}{\text{V}}_1={\text{I}}_1\left[\left(1+{\text{SR}}_{\text{5}}{\text{SC}}_{\text{gs0}}\right)\left(1+{\text{S R}}_{\text{d}}{\text{ C}}_{\text{gd0}}\right)\right]/\left[{\text{SC}}_{\text{gd0}}\left(1+{\text{SR}}_{\text{s}}{\text{C}}_{\text{gs0}}\right)\right]+{\text{SC}}_{\text{gs0}}(1+\text{S}\\ {\text{R}}_{\text{d}}{\text{C}}_{\text{gd0}})]\end{array}$$

$$\begin{array}{l}\text{So}{\text{,Y}}_{11}={\text{I}}_1/{\text{V}}_1=\left[{\text{SC}}_{\text{gd0}}\left(1+{\text{SR}}_{\text{s}}{\text{C}}_{\text{gs0}}\right)\right]+[{\text{SC}}_{\text{gs0}}(1+\text{S}{\text{R}}_{\text{s}}{\text{C}}_{\text{gs0}})]\\ \end{array}$$

$$\text{S}=\text{j}\mathrm{\omega },{\text{Y}}_{11}=\left[\left(\text{j}\mathrm{\omega }{\text{C}}_{\text{gd0}}/(1+\text{j}\mathrm{\omega }{\text{R}}_{\text{d}}{\text{C}}_{\text{gd0}}\right)\right]+\left[\text{j}\mathrm{\omega }{\text{C}}_{\text{gd0}}\right]+\left[\left(\text{j}\mathrm{\omega }{\text{C}}_{\text{gs0}}/(1+\text{j}\mathrm{\omega }{\text{R}}_{\text{s}}{\text{C}}_{\text{gs0}}\right)\right]$$

Analysis of Y ₁₁ = I ₁ /V ₁ at V ₂ = 0 $${\text{V}}_1={\text{I}}_1\left[\left({\text{R}}_{\text{s}}+1/{\text{SC}}_{\text{gs0}}\right)\left({\text{R}}_{\text{i.e}}+1/{\text{SC}}_{\text{gd0}}\right)\right]/\left[\left({\text{R}}_{\text{s}}+1/{\text{SC}}_{\text{gs0}}\right)\right]/\left[\left({\text{R}}_{\text{s}}+1/{\text{SC}}_{\text{gs0}}\right)+\left({\text{R}}_{\text{i.e}}+1/{\text{SC}}_{\text{gd0}}\right)\right]$$

$$\begin{array}{l}{\text{V}}_1={\text{I}}_1\left[\left(1+{\text{SR}}_{\text{5}}{\text{SC}}_{\text{gs0}}\right)\left(1+{\text{S R}}_{\text{i.e}}{\text{C}}_{\text{gd0}}\right)\right]/\left[{\text{SC}}_{\text{gd0}}\left(1+{\text{SR}}_{\text{s}}{\text{C}}_{\text{gs0}}\right)\right]+{\text{SC}}_{\text{gs0}}(1+\text{S}\\ {\text{R}}_{\text{i.e}}{\text{C}}_{\text{gd0}})]\end{array}$$

$$\begin{array}{l}\text{So}{\text{,Y}}_{11}={\text{I}}_1/{\text{V}}_1=\left[{\text{SC}}_{\text{gd0}}\left(1+{\text{SR}}_{\text{s}}{\text{C}}_{\text{gs0}}\right)\right]+[{\text{SC}}_{\text{gs0}}(1+\text{S}{\text{R}}_{\text{s}}{\text{C}}_{\text{gs0}})]\\ \end{array}$$

$$\text{S}=\text{j}\mathrm{\omega },{\text{Y}}_{11}=\left[\left(\text{j}\mathrm{\omega }{\text{C}}_{\text{gd0}}/(1+\text{j}\mathrm{\omega }{\text{R}}_{\text{i.e}}{\text{C}}_{\text{gd0}}\right)\right]+\left[\text{j}\mathrm{\omega }{\text{C}}_{\text{gd0}}\right]+\left[\left(\text{j}\mathrm{\omega }{\text{C}}_{\text{gs0}}/(1+\text{j}\mathrm{\omega }{\text{R}}_{\text{s}}{\text{C}}_{\text{gs0}}\right)\right]$$

Vergleichbar, Berechnung von Y₁₂ = I₁/V₂ at V₁ = 0, Y₂₁ = I₂/V₁ at V₂ = 0, Y₂₂ = I₂/V₂ at V₁ = 0 $${\text{Y}}_{12}=-\left[{\omega }^2{\text{R}}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}\right)\right]-j\omega \left[{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}\right)\right]$$

$${\text{Y}}_{21}=-\left[{\omega }^2{\text{R}}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}\right)\right]-j\omega \left[{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}\right)\right]$$

$${\text{Y}}_{22}=\left[{\omega }^2{\text{R}}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}\right)\right]+j\omega \left[{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd0}}\right)\right]$$

If you remove the imaginary part from the denominator, you get the final solution of Y ₁₁ in the form of the real and imaginary parts after the calculation: $$\begin{array}{l}{\text{Y}}_{11}={\omega }^2\left({\text{R}}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}+{\text{R}}_{\text{s}}{\text{C}}^2{}_{\text{gs0}}\right)+j\omega [\left\{{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right\}+\{{\text{C}}_{\text{gs0}}/(1+\\ {\omega }^2{\text{R}}^2{}_{\text{s}}{\text{C}}^2{}_{\text{gs0}})\}]\end{array}$$

Comparable, calculation of Y ₁₂ = I ₁ /V ₂ at V ₁ = 0, Y ₂₁ = I ₂ /V ₁ at V ₂ = 0, Y ₂₂ = I ₂ /V ₂ at V ₁ = 0 $${\text{Y}}_{12}=-\left[{\omega }^2{\text{R}}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right]-j\omega \left[{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right]$$

$${\text{Y}}_{21}=-\left[{\omega }^2{\text{R}}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right]-j\omega \left[{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right]$$

$${\text{Y}}_{22}=\left[{\omega }^2{\text{R}}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right]+j\omega \left[{\text{C}}_{\text{gd0}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd0}}\right)\right]$$

$${\text{Y}}_{21}=-j\omega {\text{C}}_{\text{gd0}}$$

$${\text{C}}_{\text{gd0}}=-\text{Im}\left({\text{Y}}_{21}\right)/\omega$$

$${\text{C}}_{\text{gs0}}=\left[\text{Im}\left({\text{Y}}_{11}\right)+\text{Im}\left({\text{Y}}_{21}\right)\right]/\omega$$

The gate overlap capacitance C _gd0 and C _gs0 can be calculated when R _s and R _d are almost zero in the off state. $${\text{Y}}_{11}=j\omega \left[{\text{C}}_{\text{gd0}}+{\text{C}}_{\text{gs0}}\right]$$

$${\text{Y}}_{21}=-j\omega {\text{C}}_{\text{gd0}}$$

$${\text{C}}_{\text{gd0}}=-\text{in the}\left({\text{Y}}_{21}\right)/\omega$$

$${\text{C}}_{\text{gs0}}=\left[\text{in the}\left({\text{Y}}_{11}\right)+\text{in the}\left({\text{Y}}_{21}\right)\right]/\omega$$

Y parameters of the extrinsic part of the circuit at zero bias, assuming R _d and R _s equal zero $$\left[\begin{array}{cc}{Y}_{11}& Y_{12}\\ Y_{21}& Y_{22}\end{array}\right]=\left[\begin{array}{cc}j\omega \left(\text{Cgd0}+\text{Cgs0}\right)& -j\omega \text{Cgd0}\\ -j\omega \text{Cgd0}& j\omega \text{Cgd0}\end{array}\right]$$

After removing the extrinsic part, the intrinsic Y ^int parameter is analyzed. The circuit is operated in the region of strong inversion.

$${\text{V}}_1={\text{I}}_1\left[\left({\text{R}}_{\text{gs}}+1/{\text{SC}}_{\text{gs}}\right)\left({\text{R}}_{\text{gd}}+1/{\text{SC}}_{\text{gd}}\right)\right]/\left[\left({\text{R}}_{\text{gs}}+1/{\text{SC}}_{\text{gs}}\right)\right]/\left[\left({\text{R}}_{\text{gd}}+1/{\text{SC}}_{\text{gd}}\right)\right]$$

$$\begin{array}{l}{\text{V}}_1={\text{I}}_1\left[\left(1+{\text{SR}}_{\text{gs}}{\text{SC}}_{\text{gs}}\right)\left(1+{\text{SR}}_{\text{gd}}{\text{ C}}_{\text{gd}}\right)\right]/\left[{\text{SC}}_{\text{gd}}\left(1+{\text{SR}}_{\text{gs}}{\text{C}}_{\text{gs}}\right)\right]+{\text{SC}}_{\text{gs}}(1+\text{S}{\text{ R}}_{\text{gd}}\\ {\text{C}}_{\text{gd}})]\end{array}$$

$$I_{11}^{int}={\text{I}}_1/{\text{V}}_1=\left[{\text{SC}}_{\text{gd}}\left(1+{\text{SR}}_{\text{gd}}{\text{C}}_{\text{gd}}\right)\right]+[{\text{SC}}_{\text{gs}}(1+\text{S}{\text{R}}_{\text{s}}{\text{C}}_{\text{gs0}})]$$

$$\text{S}=\text{j}\omega {\text{,Y}}_{11}^{int}=\left[\text{j}\omega {\text{C}}_{\text{gd}}/\left(1+\text{j}\omega {\text{R}}_{\text{gd}}{\text{C}}_{\text{gd}}\right)\right]+\left[\text{j}\omega {\text{C}}_{\text{gd}}/\left(1+\text{j}\omega {\text{R}}_{\text{gs}}{\text{C}}_{\text{gs}}\right)\right]$$

Calculation for $Y_{11}^{int},Y_{11}^{int}={\text{I}}_1/{\text{V}}_1{\text{at V}}_2=0$

$${\text{V}}_1={\text{I}}_1\left[\left({\text{R}}_{\text{gs}}+1/{\text{SC}}_{\text{gs}}\right)\left({\text{R}}_{\text{gd}}+1/{\text{SC}}_{\text{gd}}\right)\right]/\left[\left({\text{R}}_{\text{gs}}+1/{\text{SC}}_{\text{gs}}\right)\right]/\left[\left({\text{R}}_{\text{gd}}+1/{\text{SC}}_{\text{gd}}\right)\right]$$

$$\begin{array}{l}{\text{V}}_1={\text{I}}_1\left[\left(1+{\text{SR}}_{\text{gs}}{\text{SC}}_{\text{gs}}\right)\left(1+{\text{SR}}_{\text{gd}}{\text{C}}_{\text{gd}}\right)\right]/\left[{\text{SC}}_{\text{gd}}\left(1+{\text{SR}}_{\text{gs}}{\text{C}}_{\text{gs}}\right)\right]+{\text{SC}}_{\text{gs}}(1+\text{S}{\text{R}}_{\text{gd}}\\ {\text{C}}_{\text{gd}})]\end{array}$$

$$I_{11}^{int}={\text{I}}_1/{\text{V}}_1=\left[{\text{SC}}_{\text{gd}}\left(1+{\text{SR}}_{\text{gd}}{\text{C}}_{\text{gd}}\right)\right]+[{\text{SC}}_{\text{gs}}(1+\text{S}{\text{R}}_{\text{s}}{\text{C}}_{\text{gs0}})]$$

$$\text{S}=\text{j}\omega {\text{,Y}}_{11}^{int}=\left[\text{j}\omega {\text{C}}_{\text{gd}}/\left(1+\text{j}\omega {\text{R}}_{\text{gd}}{\text{C}}_{\text{gd}}\right)\right]+\left[\text{j}\omega {\text{C}}_{\text{gd}}/\left(1+\text{j}\omega {\text{R}}_{\text{gs}}{\text{C}}_{\text{gs}}\right)\right]$$

in Form des Real- und Imaginärteils: $$\begin{array}{l}{\text{Y}}_{11}^{int}={\omega }^2\left({\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+{\text{R}}_{\text{gs}}{\text{C}}^2{}_{\text{gs}}\right)+j\omega [\left\{{\text{C}}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}\right)\right\}+\{{\text{C}}_{\text{gs}}/(1+\\ {\omega }^2{\text{R}}^2{}_{\text{gs}}{\text{C}}^2{}_{\text{gs}})\}]\end{array}$$

Removing the imaginary part from the denominator gives the final solution of after calculation ${\text{Y}}_{11}^{int}$

in the form of the real and imaginary parts: $$\begin{array}{l}{\text{Y}}_{11}^{int}={\omega }^2\left({\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+{\text{R}}_{\text{gs}}{\text{C}}^2{}_{\text{gs}}\right)+j\omega [\left\{{\text{C}}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}\right)\right\}+\{{\text{C}}_{\text{gs}}/(1+\\ {\omega }^2{\text{R}}^2{}_{\text{gs}}{\text{C}}^2{}_{\text{gs}})\}]\end{array}$$

, ${\text{Y}}_{21}^{int}$

and ${\text{Y}}_{22}^{int}$

$$\begin{array}{l}{Y}_{12}^{int}=\left[{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}\right)\right]-\left[j\omega {\text{C}}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd}}\right)\right]\\ \end{array}$$

$$\begin{array}{l}{Y}_{21}^{int}=[\left({\text{g}}_{\text{m}}-j\omega {\text{g}}_{\text{m}}{\mathrm{\tau }}_{\text{m}}\right)/\left(1+{\omega }^2{\mathrm{\tau }}_m^2\right)]-[\left({\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+j\omega {\text{C}}_{\text{gd}}\right)/(1+{\omega }^2{\text{R}}^2{}_{\text{gd}}\\ {\text{C}}^2{}_{\text{gd}})]\end{array}$$

$$\begin{array}{l}{Y}_{22}^{int}=\left[{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+j\omega {\text{C}}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{d}}{\text{C}}^2{}_{\text{gd}}\right)\right]+j\omega {\text{C}}_{\text{sdx}}+[g_{ds}-\\ j\omega g_{ds}^2{L}_{sd})/\left(1+{\omega }^2{g}_{ds}^2{L}_{sd}^2\right)]\end{array}$$

The situation is similar with ${\text{Y}}_{12}^{int}$

, ${\text{Y}}_{21}^{int}$

other ${\text{Y}}_{22}^{int}$

$$\begin{array}{l}{Y}_{12}^{int}=\left[{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}\right)\right]-\left[j\omega {\text{C}}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd}}\right)\right]\\ \end{array}$$

$$\begin{array}{l}{Y}_{21}^{int}=[\left({\text{G}}_{\text{m}}-j\omega {\text{G}}_{\text{m}}{\mathrm{\tau }}_{\text{m}}\right)/\left(1+{\omega }^2{\mathrm{\tau }}_m^2\right)]-[\left({\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+j\omega {\text{C}}_{\text{gd}}\right)/(1+{\omega }^2{\text{R}}^2{}_{\text{gd}}\\ {\text{C}}^2{}_{\text{gd}})]\end{array}$$

$$\begin{array}{l}{Y}_{22}^{int}=\left[{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+j\omega {\text{C}}_{\text{gd}}/\left(1+{\omega }^2{\text{R}}^2{}_{\text{i.e}}{\text{C}}^2{}_{\text{gd}}\right)\right]+j\omega {\text{C}}_{\text{sdx}}+[G_{\mathrm{i.e}s}-\\ j\omega G_{\mathrm{i.e}s}^2{L}_{s\mathrm{i.e}})/\left(1+{\omega }^2{G}_{\mathrm{i.e}s}^2{L}_{s\mathrm{i.e}}^2\right)]\end{array}$$

and $1>>{\omega }^2{g}_{ds}^2{L}_{sd}^2$

dann sind die neuen Y^int-Parameter-Matrizen in reeller und imaginärer Form. $$Y_{11}^{int}={\omega }^2\left({\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gs}}\right)+j\omega \left({\text{C}}_{\text{gd}}+{\text{C}}_{\text{gs}}\right)$$

$$Y_{12}^{int}=-{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}-j\omega {\text{C}}_{\text{gd}}$$

$$Y_{21}^{int}={\text{g}}_{\text{m}}-{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}-j\omega \left({\text{C}}_{\text{gd}}+{\text{g}}_{\text{m}}{\mathrm{\tau }}_{\text{m}}\right)$$

$$Y_{22}^{int}={\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+g_{ds}+j\omega \left({\text{C}}_{\text{gd}}+{\text{C}}_{\text{sdx}}-g_{ds}^2{L}_{sd}\right)$$

All parameters are calculated in the ON state of the device. Now the Y ^int parameter is simplified by making some assumptions: 1 >>>> ω ² R ² _gd C ² _gd , 1 >> ω ² R ² _gs C ² _gs , $1>>{\omega }^2{\mathrm{right}}_m^2$

other $1>>{\omega }^2{G}_{\mathrm{i.e}s}^2{L}_{s\mathrm{i.e}}^2$

then the new Y ^int parameter matrices are in real and imaginary form. $$Y_{11}^{int}={\omega }^2\left({\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gs}}\right)+j\omega \left({\text{C}}_{\text{gd}}+{\text{C}}_{\text{gs}}\right)$$

$$Y_{12}^{int}=-{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}-j\omega {\text{C}}_{\text{gd}}$$

$$Y_{21}^{int}={\text{G}}_{\text{m}}-{\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}-j\omega \left({\text{C}}_{\text{gd}}+{\text{G}}_{\text{m}}{\mathrm{\tau }}_{\text{m}}\right)$$

$$Y_{22}^{int}={\omega }^2{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}+G_{\mathrm{i.e}s}+j\omega \left({\text{C}}_{\text{gd}}+{\text{C}}_{\text{sdx}}-G_{\mathrm{i.e}s}^2{L}_{s\mathrm{i.e}}\right)$$

The above equations contain the parameters for all small signals of the proposed fin FET in the strong inversion regime. The intrinsic parameters are extracted from the Y-parameter simulation results. The value of the intrinsic parameters can be determined as follows: $${\text{C}}_{\text{gd}}=-\text{in the}\left(Y_{12}^{int}\right)/\omega$$

For the calculation of the gate-source capacitance (C _gs ), $${\text{C}}_{\text{gd}}=-\text{in the}\left(Y_{12}^{int}\right)/\omega$$

$${\text{R}}_{\text{gs}}=\frac{1}{C_{gs}^2}\left[\frac{Re\left(Y_{11}^{int}\right)}{\omega 2}-{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}\right]$$

$${\text{g}}_{\text{m}}=\text{Re}\left(Y_{21}^{int}\right)\text{ at }{\omega }^2=0$$

$${\text{g}}_{ds}=\text{Re}\left(Y_{22}^{int}\right)\text{ at }{\omega }^2=0$$

$${\tau }_m=\frac{1}{g_m}\left[\frac{-Im\left(Y_{21}^{int}\right)}{\omega }-{\text{C}}_{\text{gd}}\right]$$

$$L_{sd}={\tau }_m/g_{ds}$$

$${\text{C}}_{\text{sdx}}=\frac{Im\left(Y_{22}^{int}\right)}{\omega }-{\text{C}}_{\text{gd}}-L_{sd}{g}_{ds}^2$$

The same applies to the calculation of R _gd , R _gs , g _m ,g _ds , τ _m , C _sdx and L _sd $${\text{R}}_{\text{gd}}=-\text{re}\left(Y_{12}^{int}\right)/{\omega }^2{C}^2{}_{\text{gd}}$$

$${\text{R}}_{\text{gs}}=\frac{1}{C_{Gs}^2}\left[\frac{Re\left(Y_{11}^{int}\right)}{\omega 2}-{\text{R}}_{\text{gd}}{\text{C}}^2{}_{\text{gd}}\right]$$

$${\text{G}}_{\text{m}}=\text{re}\left(Y_{21}^{int}\right)\text{at}{\omega }^2=0$$

$${\text{G}}_{\mathrm{i.e}s}=\text{re}\left(Y_{22}^{int}\right)\text{at}{\omega }^2=0$$

$${\tau }_m=\frac{1}{G_m}\left[\frac{-Im\left(Y_{21}^{int}\right)}{\omega }-{\text{C}}_{\text{gd}}\right]$$

$$L_{s\mathrm{i.e}}={\tau }_m/G_{\mathrm{i.e}s}$$

$${\text{C}}_{\text{sdx}}=\frac{Im\left(Y_{22}^{int}\right)}{\omega }-{\text{C}}_{\text{gd}}-L_{s\mathrm{i.e}}{G}_{\mathrm{i.e}s}^2$$

The BQP model is derived from pure physics and allows an approximation of the quantum behavior of different device classes and a range of materials. The effects of quantum confinement on device performance, including I-V properties, are then calculated to a good approximation.

wobei Q das Bohmsche Quantenpotential und n und p die Elektronen- bzw. Lochkonzentration sind.Here, positive values of EBQP indicate higher electron density at the center of the channel and negative values of EBQP indicate lower electron density at the edge of the channel. The electron and hole concentration for the BQP model is given by the following equation: $$\text{n}={\text{N}}_{\text{c}}\text{ex}\left(-\frac{E_c+qQ}{kT}\right)\text{and p}={\text{N}}_{\text{v}}\text{ex}\left(-\frac{qQ-E_v}{kT}\right)$$

where Q is the Bohmian quantum potential and n and p are the electron and hole concentrations, respectively.

The DG n-FinFET is rated at α=0.22, 0.24, and α=0.26 on the logarithmic scale for various high-k materials. The high-k gate materials have good channel controllability, which is why the drain current ramps up to the clipping voltage (V _gs -V _th ) and then saturates. The drain voltage is held at 600 mV to measure the I _on /I _off current ratio. I _ON is examined at a gate voltage (V _gs ) = 0.9 V and I _OFF is measured at V _gs = 0 V. The device drive capability is about 0.2 mA at a gate overdrive voltage (V _ov =V _gs -V _th ) of 0.53 V for TiO ₂ DG n-FinFET at α = 0.24. The TiO ₂ DG n-Fin FET has better SS, DIBL and higher I _ON /I _OFF ratio compared to SiO ₂ DG n-Fin FET and HfO ₂ DG n-Fin FET.

The sub-threshold swing for various gate dielectric materials with the gate oxide thickness as a fixed parameter. As the dielectric constant increases, the sub-threshold excursion decreases. As the dielectric constant increases, the rate of change of the subthreshold swing decreases with the rate of change of the gate oxide film thickness. This is because the off current decreases as the dielectric constant increases. Therefore, the on-off current ratio increases with increasing dielectric constant and transistor performance is improved. The sub-threshold swing varies for different gate dielectric materials, namely silicon oxide (SiO ₂ , k=3.9), hafnium oxide (HfO ₂ , k=21) and titanium dioxide (TiO ₂ , k=80). In this device, SS and DIBL decrease as the value of the gate dielectric increases. The SS and DIBL values are shown in Table 2 in comparison. Table 2: Comparison of SS, DIBL and I _ON /I _OFF current ratio for DG n-Fin FET with different gate dielectric materials. Dielectric gate materials Matching parameters (a) Sub-Threshold Swing (mV/decade) DIBL (mV/V) Threshold voltage (Vth) in volts I _ON /I _OFF ratio SiO2 ( _k =3.9) α = 0.22 70.48 32 0.334 2.4x10 ⁸ α = 0.24 70.97 32 0.333 1.92× ¹⁰⁸ α = 0.26 71.46 30.4 0.332 1.45x10 ⁸ HfO ₂ (k=21) α = 0.22 58.04 12 0.365 0.64x10 ¹⁰ α = 0.24 55.03 11.2 0.363 0.45x10 ¹⁰ α = 0.26 51.84 10.8 0.364 0.32x10 ¹⁰ _TiO2 (k=80) α = 0.22 51.49 10 0.370 0.11×10 ¹¹ α = 0.24 46.46 10 0.369 0.85x10 ¹⁰ α = 0.26 46.5 8th 0.369 0.32x10 ¹⁰

The change in sub-threshold swing with respect to the adjustment parameter varies from α = 0.2 to 0.3. In the BQP model equation, the fitting parameter (α) essentially depends on the device size as well as the supply voltage, and SS also depends on Vgs. It was observed that the sub-threshold swing decreases from 58.36 mV/dec to 33.6 mV/dec when α varies between 0.2 and 0.3 for the TiO ₂ gate dielectric material. However, the best value for α is 0.24 for the subthreshold current. With α equal to 0.24, the SS value of 46.46 mV/decade for the TiO ₂ gate dielectric materials is better than the SS value of 55.03 mV/decade for the HfO ₂ gate dielectric materials.

The non-quasi-static small-signal parameters of the DG n-Fin FET are extracted using the direct extraction method. The extrinsic gate-source (C _gs0 ) and gate-drain capacitances (C _gd0 ) are extracted from the Y-parameter data using the 3D Silvaco simulator at zero bias. The value of C _gs0 is 19.7 aF and C _gd0 is 27aF. The other intrinsic parameters such as intrinsic capacitances (C _gs , C _gd , C _sdx ), distributed channel resistances (R _gs , R _gd ), τ _m and L _sd were extracted at Vgs = IV, Vds = 0.6V. These intrinsic parameters extracted from the Y parameters are nearly constant with frequency. Table.3: Extracted parameters of DG n-FinFET at Vgs = IV, Vds = 0.6V. parameter values (units) parameter values (units) _gm 2.52mS C _gd 50.7 aF g _ds 0.204mS R _gs 95Ω C _gs0 19.7aF R _gd 56Ω _Cgd0 27.0 aF τ _m 9.25fsec C _sdx 2.08 aF L _sd 0.045nH C _gs 48.1 old version

and ${\omega }^2{g}_{ds}^2{L}_{sd}^2$

werden wie folgt berechnet 1.4×10^-3, 4.8×10^-3, 15.63×10^-3, and 15.3×10^-3 unter 2500 GHz, bzw.. Diese Ergebnisse bestätigen die Annahme, dass die Werte im obigen Abschnitt gültig sind. Der Fehler zwischen berechneten und simulierten Y-Parametern beträgt nur 1.5 % bis 2500 GHz im Sättigungsbereich, was mehr als das Zweifache der Grenzfrequenz ist.The values of ω ² R ² _gd C ² _gd , ω ² R ² _gs C ² _gs , ${\omega }^2{\tau }_m^2$

other ${\omega }^2{G}_{\mathrm{i.e}s}^2{L}_{s\mathrm{i.e}}^2$

are calculated as 1.4×10 ^-3 , 4.8×10 ^-3 , 15.63×10 ^-3 , and 15.3×10 ^-3 below 2500 GHz, respectively. These results confirm that the values in the section above are valid. The error between calculated and simulated Y-parameters is only 1.5% up to 2500 GHz in the saturation region, which is more than twice the cut-off frequency.

The transconductance (g _m ) behavior of the DG n-Fin FET is simulated with the silvaco tools using the BQP model at Vds = 0.6 V. Initially the gm increases up to Vgs = 0.66 volts. Due to the inversion current (Iinv), it starts contributing to Ids. After Vgs = 0.66 volts it decreases because the overdrive voltage (V _gs - V _th ) increases at constant Ids, which means that gm is inversely proportional to the overdrive voltage (V _gs -V _th ). The transconductance of TiO ₂ is higher than the transconductance of HfO ₂ and SiO ₂ based DG n-Fin FET.

The high-frequency capacitances such as gate-to-source capacitance (C _gs ) and gate-to-drain capacitance (C _gd ) for n-fin FET versus gate-to-source voltage at a drain voltage of V _ds = 600mV. The simulated gate-to-source capacitance (C _gs ) and gate-to-drain capacitance (C _gd ) results are 78.5 aF and 83.4 aF, respectively, for the proposed device. For the analog/RF performance (likes, f _τ and intrinsic delay) of the devices, the capacitance value (C _gg ) should be lower. A lower capacitance (C _gg ) provides a better intrinsic cutoff frequency (f _τ ).

For RF applications, the unity gain cutoff frequency (f _τ ) is a very important parameter to study. The f _τ equation is given $${\text{f}}_{\text{T}}=\frac{G_m}{2\pi c_{GG}}$$

, wenn $${\text{f}}_{\text{T}}=\frac{{\mu }_n\text{Cox}\frac{W_{eff}}{L}\left(\text{Vgs}-\text{Vth}\right)}{2\pi c_{gg}}$$

$${\text{f}}_{\text{T}}=\frac{{\mu }_n\left(\text{Vgs}-\text{Vth}\right)}{2\pi L^2},\left({\text{where C}}_{\text{gg}}={\text{C}}_{\text{ox}}\text{WL}\right)$$

$${\text{f}}_{\text{T}}=\frac{{\mathrm{\mu }}_{\text{n}}{\text{E}}_{\text{ch}}}{2\mathrm{\pi }\text{L}}=\frac{{\text{v}}_{\text{d}}}{2\mathrm{\pi }\text{L}}=\frac{1}{2\mathrm{\pi }{\mathrm{\tau }}_{\text{t}}}$$

It is known that ${\text{G}}_{\text{m}}=\frac{\partial I_{\mathrm{i.e}s}}{\partial V_{Gs}}={\mu }_n{\text{C}}_{\text{ox}}\frac{W_{eff}}{L}\left({\text{V}}_{\text{gs}}-{\text{V}}_{\text{th}}\right)$

, if $${\text{f}}_{\text{T}}=\frac{{\mu }_n\text{cox}\frac{W_{eff}}{L}\left(\text{vs}-\text{Vth}\right)}{2\pi c_{GG}}$$

$${\text{f}}_{\text{T}}=\frac{{\mu }_n\left(\text{vs}-\text{Vth}\right)}{2\pi L^2},\left({\text{where C}}_{\text{vs}}={\text{C}}_{\text{ox}}\text{WL}\right)$$

$${\text{f}}_{\text{T}}=\frac{{\mathrm{\mu }}_{\text{n}}{\text{E}}_{\text{ch}}}{2\mathrm{\pi }\text{L}}=\frac{{\text{v}}_{\text{i.e}}}{2\mathrm{\pi }\text{L}}=\frac{1}{2\mathrm{\pi }{\mathrm{\tau }}_{\text{t}}}$$

where gm is the transconductance and c _gg is the gate-to-gate capacitance. The value of c _gg is the sum of c _gs and c _ds , Weff is the effective blade width (W _eff = 2H _fin ) and τ _t is the transit time. The higher f _τ is suitable for the high speed of the device, since a small gate length enables a low transit time.

Another important parameter is the intrinsic gate delay (τ _int ). It represents the cut-off frequency of transistor operation. The equation for τ _int is written for the n-type FinFET in terms of the parasitic gate capacitance (C _gg ) as follows $${\text{T}}_{\text{internal}}=\frac{C_{GG}\times V_{\mathrm{i.e}\mathrm{i.e}}}{I_{\mathrm{i.e}s}}$$

Where τ _int represents the intrinsic gate delay, it can be seen that the delay for high-k (k= 80) n-fin FETs at α = 0.24 is less than α = 0.22 and 0.26 at low V _ds values . At this V _ds value, _ION increases. After this V _ds value, the drain current becomes constant as V ds increases again, and also Cgg reaches its maximum value in accumulation mode at flat band voltage (V _FB ). This increases the inherent delay a little. For low-power applications, this α = 0.24 model is well suited because it has a lower intrinsic gate delay than other values of α.

Another important parameter is the off-state power dissipation. The off-state power dissipation is calculated by PD = I _OFF × V _dd . This parameter indicates that high V _dd devices have higher power dissipation. Table 4 shows the comparison of the analog/RF parameters (ie f _τ , _Tint and PD) with different values of α. Table 4: Comparison of f _τ , PD and τ _int for TiO ₂ n-FinFET at different values of α Matching parameters (α) cut-off frequency , fτ (GHz ₎ Off-state power dissipation , PD (fW) Intrinsic gate delay , τ _int (ps) α = 0.22 1392.60 12 0.95 α = 0.24 1394.5 8.04 0.42 α = 0.26 1390 11 0.94

It has been found that the BQP model is used in the physics part of the 3D Devedit Silvaco simulator to calculate the sub-threshold swing, DIBL, gm, intrinsic gate delay and off-state power dissipation at different values of a fitting parameter (a = 0.22, 0.24 and 0.26). In the proposed system, the channel is lightly doped since the doped channel reduces the effect of impact ionization; hence the sub-threshold swing decreases. At 1 nm gate oxide thickness, the TiO ₂ DG n-Fin FET at α = 0.24 has a low DIBL of 10 mV/V, a sub-threshold swing of 46.46 mV/dec, a drive current of 0.2 mA and a leakage current of 13fA is achieved. Compared to density gradient methods, the main advantages of this BQP model are that both Maxwell-Boltzmann and Fermi-Dirac statistics are included, an independent transport model is used, and there is better fitting and calibration.

NQS modeling of a DG n-fin FET in the strong inversion region was also successfully performed. The intrinsic parameters were extracted from the Y parameters after removing the C _gs0 , C _{gd0 ,} Rs and Rd. The error between the calculated and the simulated Y-parameter is 2% in the saturation range up to 2500 THz. The proposed system is used for digital switching applications and also for RF applications up to the cut-off frequency due to the low subthreshold swing.

The figures and the preceding description give examples of embodiments. Those skilled in the art will understand that one or more of the elements described may well be combined into a single functional element. Alternatively, certain elements can be broken down into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, the order of the processes described herein may be changed and is not limited to the manner described herein. Additionally, the actions of a flowchart need not be performed in the order shown; Also, not all actions have to be carried out. Also, those actions that are not dependent on other actions can be performed in parallel with the other actions. The scope of the embodiments is in no way limited by these specific examples. Numerous variations are possible, regardless of whether they are explicitly mentioned in the description or not, e.g. B. Differences in structure, dimensions and use of materials. The scope of the embodiments is at least as broad as indicated in the following claims.

Advantages, other benefits, and solutions to problems have been described above with respect to particular embodiments. However, the benefits, advantages, problem solutions, and components that can cause an advantage, benefit, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or component of any or all claims.

reference list

100

A system for developing and analyzing at least one parameter of a Bohm quantum potential (Bqp) device.

102

Goal

104

source contact

104b

drain contact

106

dielectric layer

202

Back gate

204

channel

206

Front gate

208

source

210

drainage

212

intrinsic layer

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• KR 100748261 B1 [0006]
• US 6812119 B1 [0007]
• US 6885055 B2 [0008]

Claims (6)

A system (100) for developing and analyzing at least one parameter of a Bohm quantum potential (BQP) device, the BQP device of the system (100) comprising: a gate (102) of a first material to avoid depletion effects; a source and a drain contact (104a, 104b), each made of a second material; and a pair of dielectric layers (106) composed of a third material, the pair of dielectric layers being disposed on either side of the source and drain contacts (104a, 104b), resulting in the formation of a channel. system after claim 1 wherein the first material to form the gate (102) is titanium nitride (TiN) having a work function of 4-5eV. system after claim 1 , wherein the second material for forming the source and drain contacts (104a, 104b) is an aluminum electrode with an n-type doping concentration (10 ¹⁹ cm ^-3 ), while the channel has a lightly doped p-type doping concentration (10 ¹⁶ cm ^-3 ). . system after claim 1 , where the gate resistance is analyzed by determining either the Y or Z parameter at high frequency from a small-signal non-quasi-static (NQS) device. system after claim 4 , where the NQS small-signal device consists of an intrinsic and an extrinsic part, where the intrinsic part contains bias-dependent elements and the extrinsic part contains bias-independent elements. system after claim 5 , where a variety of extrinsic parameters are first calculated by a calculation module to obtain gate-source and gate-drain capacitances at zero bias, where the intrinsic Y parameter is calculated at strong inversion.

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