Modeling method and device for two-dimensional material field effect transistor

Abstract

This application relates to a modeling method and apparatus for two-dimensional material field-effect transistors (FETs). The method includes: determining the coordinate intervals of the source junction, intrinsic channel, and drain junction based on the device structure and electrical characteristics test bias configuration information of the FET; establishing a mathematical model of the Landauer carrier transport physical landscape of the source and drain junctions according to the defined coordinate intervals; and generating the current transport of the source junction, intrinsic channel, and drain junction in the quasi-Fermi level phase space (QFLPS) form using preset Landauer formulas and preset drift-diffusion formulas, respectively, to obtain a comprehensive formula for the current. This solves the problems in related technologies, such as calculating the final junction-channel series current by solving the internal node voltage using Kirchhoff's current conservation law, which severely affects computational efficiency and fails to meet the efficiency requirements of circuit simulation; and the parallel weighted average method lacking physical meaning and hindering the evaluation of the process based on experimental results from a physical perspective.

Description

Technical Field

[0001] This application relates to the field of transistor technology, and in particular to a modeling method and apparatus for two-dimensional material field-effect transistors. Background Technology

[0002] Two-dimensional materials, which have emerged in recent years, are considered to be one of the most promising alternatives to silicon for ultra-small semiconductor devices. Two-dimensional materials as channel materials for field-effect transistors are receiving increasing attention and research.

[0003] In related technologies, in order to continuously describe the characteristics of ohmic and Schottky contacts, two modeling techniques can be used. The first is the equivalent parasitic resistance method, which treats the junction as equivalent to the parasitic resistance connected in series across the intrinsic channel. The second is to calculate the junction transport current and the intrinsic channel transport current separately and then calculate the weighted average in parallel.

[0004] However, the final junction-channel series current can only be calculated by solving the internal node voltages using Kirchhoff's current conservation law, which severely affects computational efficiency and fails to meet the efficiency requirements of circuit simulation. Furthermore, since the junction and channel essentially influence each other in a series configuration, the method of taking a weighted average by connecting them in parallel (so that the terminal voltages of all components are known, and there is no need to solve the nonlinear equations caused by Kirchhoff's law) has no physical meaning and is not conducive to evaluating the process based on experimental results from a physical perspective. This method urgently needs improvement. Summary of the Invention

[0005] This application provides a modeling method and apparatus for two-dimensional material field-effect transistors to solve the problems in related technologies, such as the calculation of the final junction-channel series current by solving the internal node voltage using Kirchhoff's current conservation law, which seriously affects the calculation efficiency and does not meet the efficiency requirements of circuit simulation. Furthermore, since the junction and channel essentially influence each other in a series configuration, the method of taking a weighted average in parallel has no physical meaning and is not conducive to evaluating the process from a physical perspective based on experimental results.

[0006] The first aspect of this application provides a modeling method for a two-dimensional material field-effect transistor, comprising the following steps: determining the coordinate intervals of the source junction, intrinsic channel, and drain junction of the channel based on the device structure and electrical characteristics test bias configuration information of the two-dimensional material field-effect transistor; establishing a mathematical model of the Landauer carrier transport physical landscape of the source junction and drain junction according to the divided coordinate intervals; and generating the current transport of the source junction, intrinsic channel, and drain junction in the form of quasi-Fermi level phase space (QFLPS) using the preset Landauer formula and the preset drift diffusion formula, respectively, to obtain a comprehensive formula for the current.

[0007] Optionally, in one embodiment of this application, the mathematical model for establishing the Landauer carrier transport physical picture of the source junction and the drain junction based on the coordinate intervals of the source junction, intrinsic channel, and drain junction includes: establishing a first mathematical model of the transmission energy spectrum based on the carrier transport mechanism at the band edge transition; generating the DOM function energy spectrum based on the number of collective momentum modes contained in the electrons of the source junction per unit spatial scale at a preset energy level; establishing a second mathematical model that reflects the Maxwell-Boltzmann distribution at equilibrium and reflects the effect of applying drain-source bias voltage to move the overall kinetic energy to a higher level; and obtaining the physical model formulas for the internal transmittance and collective kinetic energy spectrum based on the first mathematical model, the DOM function energy spectrum, and the second mathematical model.

[0008] Optionally, in one embodiment of this application, the first mathematical model is:

[0009] Γ es (E)=exp(-2γ+Λ(EE cs ) / φ t,es ),

[0010] in, It is derived from the WKB approximation used to describe the tunneling process. q represents Planck's constant, and q represents the elementary charge. Represents the effective electron mass, ρ s Represents the local effective charge density, ∈ s E represents the dielectric constant of a semiconductor. cs The conduction band bottom of the semiconductor channel is represented by E, which represents the electron energy, and Λ(x) represents the ramp function. t,es Represents the electron injection barrier of the injection source junction;

[0011] The energy spectrum of the DOM function is:

[0012]

[0013] Among them, g v For the sake of simplifying and measuring, K is the effective mass of the source junction electrons. es (E) represents the collective kinetic energy spectrum of the source junction electrons;

[0014] The second mathematical model is:

[0015]

[0016] Among them, E b,es V represents ds The ground state kinetic energy when φ = 0 a,es T represents the source junction electron accelerating barrier. sThis represents the source junction temperature.

[0017] Optionally, in one embodiment of this application, the mathematical model for the Landauer-QFLPS carrier transport physics, which integrates the effects of source junction, drain junction, and channel transport characteristics, is as follows:

[0018]

[0019] The limits of integration of the formula are set as follows:

[0020] E Fs =0,

[0021] E Fd =-qV ds ,

[0022] Among them, V gs V represents the gate-source voltage. ds Represents the drain-source voltage, μ n Represents electron mobility, μ p Represents hole mobility, φ′ n Represents the effective electron threshold voltage, φ p ′ represents the effective hole threshold voltage, φ t η represents the channel thermal barrier. es η represents the source-junction electron current limiting index. hd φ represents the drain-hole junction current limiting index. a,es Represents the electron acceleration barrier of the source junction, φ a,hd The hole acceleration barrier represents the junction-hole accelerator; where q represents the elementary charge, W and L represent the channel width and length, respectively, and E... Fn Represents the quasi-Fermi level of electrons, E Fp Represents the hole quasi-Fermi level, E Fs Represents the source-end Fermi level, E Fd Represents the drain-end Fermi level, where n represents the electron concentration and p represents the hole concentration; and n and p are related to E Fn and E Fp The functional relationship is given by the following system of equations;

[0023] q 2 (np) / C ox Ψ+qV gs =0

[0024]

[0025]

[0026] E Fn =E Fp ,

[0027] Where Ψ represents the electrostatic potential energy of the channel surface (also determined by the self-consistency of the above equation), C ox D represents the surface density of the gate oxide capacitance. e and D h These represent the energy state densities of conduction band electrons and valence band holes, respectively.

[0028] Optionally, in one embodiment of this application, the method further includes: constructing a linearized Gaussian wavelet function over a preset sampling interval to solve a preset optimization problem, and searching a parameter optimization network in parallel to obtain a second-order tensor Y input model for circuit simulation.

[0029] A second aspect of this application provides a modeling apparatus for a two-dimensional material field-effect transistor (FET), comprising: a determination module for determining the coordinate intervals of the source junction, intrinsic channel, and drain junction of the channel based on the device structure and electrical characteristics test bias configuration information of the FET; a modeling module for establishing a mathematical model of the Landauer carrier transport physical landscape of the source junction and drain junction based on the coordinate intervals of the source junction, intrinsic channel, and drain junction; and an acquisition module for generating the current transport of the source junction, intrinsic channel, and drain junction in the form of a quasi-Fermi level phase space (QFLPS) using a preset Landauer formula and a preset drift-diffusion formula, respectively, to obtain a comprehensive formula for the current.

[0030] Optionally, in one embodiment of this application, the modeling module includes: a first establishment unit, used to establish a first mathematical model of the transmission energy spectrum based on the carrier transport mechanism at the band edge transition;

[0031] The generation unit is used to generate the DOM function energy spectrum based on the number of collective momentum modes contained in the source-junction electrons per unit spatial scale at a preset energy level; the second establishment unit is used to establish a second mathematical model that reflects the Maxwell-Boltzmann distribution at equilibrium and reflects the effect of applying a drain-source bias voltage to move the overall kinetic energy to a higher level; the acquisition unit is used to obtain the physical model formulas of the internal transmittance and collective kinetic energy spectrum according to the first mathematical model, the DOM function energy spectrum and the second mathematical model.

[0032] Optionally, in one embodiment of this application, the first mathematical model is:

[0033] Γ es (E)=exp(-2γ+Λ(EE cx ) / φ t,es ),

[0034] in, It is derived from the WKB approximation used to describe the tunneling process. q represents Planck's constant, and q represents the elementary charge. Represents the effective electron mass, ρ s Represents the local effective charge density, ∈ s E represents the dielectric constant of a semiconductor. cs The conduction band bottom of the semiconductor channel is represented by E, which represents the electron energy, and Λ(x) represents the ramp function. t,es Represents the electron injection barrier of the injection source junction;

[0035] The energy spectrum of the DOM function is:

[0036]

[0037] Among them, g v For the sake of simplifying and measuring, K is the effective mass of the source junction electrons. es (E) represents the collective kinetic energy spectrum of the source junction electrons;

[0038] The second mathematical model is:

[0039]

[0040] Among them, E b,es V represents ds The ground state kinetic energy when φ = 0 a,es T represents the source junction electron accelerating barrier. s This represents the source junction temperature.

[0041] Optionally, in one embodiment of this application, the mathematical model for the Landauer-QFLPS carrier transport physics, which integrates the effects of source junction, drain junction, and channel transport characteristics, is as follows:

[0042]

[0043] The limits of integration of the formula are set as follows:

[0044] E Fs =0,

[0045] E Fd =-qV ds ,

[0046] Among them, V gs V represents the gate-source voltage. ds Represents the drain-source voltage, μ n Represents electron mobility, μ p Represents hole mobility, φ′ n Represents the effective electron threshold voltage, φ′ p Represents the effective hole threshold voltage, φ t η represents the channel thermal barrier. es η represents the source-junction electron current limiting index. hdφ represents the drain-hole junction current limiting index. a,es Represents the electron acceleration barrier of the source junction, φ a,hd The hole acceleration barrier represents the junction-hole accelerator; where q represents the elementary charge, W and L represent the channel width and length, respectively, and E... Fn Represents the quasi-Fermi level of electrons, E Fp Represents the hole quasi-Fermi level, E Fs Represents the source-end Fermi level, E Fd Represents the drain-end Fermi level, where n represents the electron concentration and p represents the hole concentration; and n and p are related to E Fn and E Fp The functional relationship is given by the following system of equations;

[0047]

[0048]

[0049]

[0050] E Fn =E Fp ,

[0051] Where Ψ represents the electrostatic potential energy of the channel surface (also determined by the self-consistency of the above equation), C ox D represents the surface density of the gate oxide capacitance. e and D h These represent the energy state densities of conduction band electrons and valence band holes, respectively.

[0052] Optionally, in one embodiment of this application, it further includes: a construction module, used to construct a linearized Gaussian wavelet function on a preset sampling interval to solve a preset optimization problem, and to search a parameter optimization network in parallel to obtain a second-order tensor Y input model for circuit simulation.

[0053] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the modeling method for two-dimensional material field-effect transistors as described in the above embodiments.

[0054] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described modeling method for two-dimensional material field-effect transistors.

[0055] This application provides a continuous description of the modeling technology for two-dimensional material field-effect transistors (FETs) with ohmic and Schottky contacts, along with its corresponding parameter extraction algorithm. Based on this model and algorithm, on the one hand, model extraction can be performed on experimentally fabricated two-dimensional material FETs to analyze parameter dispersion and thus conduct process evaluation. On the other hand, it can be directly applied to model-based circuit simulation, improving computational efficiency and meeting the efficiency requirements of power simulation. This solves the problems in related technologies, such as calculating the final junction-channel series current by solving the internal node voltage using Kirchhoff's current conservation law, which severely affects computational efficiency and fails to meet the efficiency requirements of circuit simulation. Furthermore, since the junction and channel essentially influence each other in a series configuration, the method of taking a weighted average in parallel has no physical meaning and is not conducive to evaluating the process from a physical perspective based on experimental results.

[0056] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0057] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0058] Figure 1 This is a flowchart illustrating a modeling method for a two-dimensional material field-effect transistor according to an embodiment of this application;

[0059] Figure 2 This is a schematic diagram of a device and test structure for a modeling method of a two-dimensional material field-effect transistor according to an embodiment of this application;

[0060] Figure 3 This is a schematic diagram of the band structure of a modeling method for a two-dimensional material field-effect transistor according to an embodiment of this application;

[0061] Figure 4 This is a schematic diagram illustrating the principle of the mathematical model of the transmittance of the electron current component in a modeling method for a two-dimensional material field-effect transistor according to an embodiment of this application.

[0062] Figure 5 This is a schematic diagram of the mathematical model principle of the collective kinetic energy spectrum of electrons in a modeling method for a two-dimensional material field-effect transistor according to an embodiment of this application.

[0063] Figure 6 This is a schematic diagram of the model parameter extraction algorithm of a modeling method for a two-dimensional material field-effect transistor according to an embodiment of this application;

[0064] Figure 7This is a schematic diagram of a modeling device for a two-dimensional material field-effect transistor according to an embodiment of this application;

[0065] Figure 8 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0066] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0067] The following describes a modeling method and apparatus for two-dimensional material field-effect transistors (FETs) according to embodiments of this application, with reference to the accompanying drawings. Addressing the issues raised in the background section, where the final junction-channel series current is calculated by applying Kirchhoff's current conservation law to the internal node voltage, severely impacts computational efficiency and fails to meet the efficiency requirements of circuit simulation, and where the parallel weighted average method lacks physical meaning due to the inherent series interaction between the junction and channel, hindering the evaluation of the process based on experimental results from a physical perspective, this application provides a modeling method for two-dimensional material field-effect transistors. This method continuously describes the modeling techniques for Ω-contact and Schottky-contact FETs and their associated parameter extraction algorithms. Based on this model and algorithm, on the one hand, model extraction can be performed on experimentally fabricated FETs to analyze parameter dispersion and thus conduct process evaluation; on the other hand, it can be directly applied to model-based circuit simulation, improving computational efficiency and meeting the efficiency requirements of power simulation. This solves the problems in related technologies, such as the serious impact on calculation efficiency and failure to meet the efficiency requirements of circuit simulation when calculating the final junction-channel series current by solving the internal node voltage using Kirchhoff's current conservation law. Furthermore, since the junction and channel essentially influence each other in series, the method of taking a weighted average in parallel has no physical meaning and is not conducive to evaluating the process from a physical perspective based on experimental results.

[0068] Specifically, Figure 1 This is a schematic flowchart illustrating a modeling method for a two-dimensional material field-effect transistor provided in an embodiment of this application.

[0069] like Figure 1 As shown, the modeling method for this two-dimensional material field-effect transistor includes the following steps:

[0070] In step S101, based on the device structure and electrical characteristics test bias configuration information of the two-dimensional material field-effect transistor, the coordinate range of the source junction, intrinsic channel and drain junction of the channel is determined.

[0071] In actual implementation, the embodiments of this application may consider the device structure and electrical characteristic test bias configuration information of two-dimensional material field-effect transistors, such as... Figure 2 As shown, the circuit passes through three terminals: gate (G), source (S), and drain (D), where the current I... ds The water flows from the drain (D) through the channel (made of two-dimensional material) into the source (S). This transport process is regulated by changing the gate (G) voltage, thereby dividing the channel into three segments: (i) the source junction, (ii) the intrinsic channel, and (iii) the drain junction. This determines the coordinate intervals of the source junction, intrinsic channel, and drain junction, denoted as [x...]. s ,x si ], [x si ,x di ] and [x di ,x d ].

[0072] The embodiments of this application can determine the coordinate range of the source junction, intrinsic channel and drain junction of the channel based on the device structure and electrical characteristics test bias configuration information of the two-dimensional material field-effect transistor. This provides a basis for the subsequent establishment of a mathematical model of the Landauer carrier transport physical picture of the source junction and drain junction, as well as the final comprehensive formula, namely the Landauer-QFLPS formula, thereby improving the physical reliability and computational efficiency of the model.

[0073] The Landauer equation for source-junction electron transport is as follows:

[0074]

[0075] Where W represents the channel width and q is the elementary charge. To reduce Planck's constant, Γ es (E) is the transmission energy spectrum of electrons injected at the source end, M es (E) represents the mode density energy spectrum (DOM), f F.D. (E,E F ):=(1+exp(EE) F ) / kT) -1 The distribution follows the Fermi-Dirac distribution, where k represents the Boltzmann constant, T represents temperature, and E... Fni E represents the value of the quasi-Fermi level at the intrinsic channel interface. Fpi This is the value of the hole quasi-Fermi level at the intrinsic channel interface.

[0076] In step S102, a mathematical model of the Landauer carrier transport physical picture of the source junction and the drain junction is established based on the divided coordinate interval.

[0077] In actual implementation, the embodiments of this application can establish a mathematical model of the Landauer carrier transport physical landscape of the source junction and the drain junction based on the coordinate interval of the source junction, intrinsic channel and drain junction, thereby continuously describing the two-dimensional material field-effect transistor modeling technology of Ohmic contact and Schottky contact and its supporting parameter extraction algorithm, taking into account both physical reality and computational efficiency, and improving the physical reliability and computational efficiency of the model.

[0078] Optionally, in one embodiment of this application, a mathematical model of the Landauer carrier transport physical picture of the source junction is established based on the coordinate intervals of the source junction, intrinsic channel, and drain junction. This includes: establishing a first mathematical model of the transmission energy spectrum based on the carrier transport mechanism at the band edge transition; generating the DOM function energy spectrum based on the number of collective momentum modes contained in the source junction electrons per unit spatial scale at a preset energy level; establishing a second mathematical model that reflects the Maxwell-Boltzmann distribution at equilibrium and reflects the effect of applying drain-source bias voltage to move the overall kinetic energy to a higher level; and obtaining the physical model formulas for the internal transmittance and collective kinetic energy spectrum based on the first mathematical model, the DOM function energy spectrum, and the second mathematical model.

[0079] In some embodiments, the transmission energy spectrum Γ can be established based on the carrier transport mechanism at the band edge transition. es The first mathematical model of (E); based on the number of collective momentum modes contained in the source junction electrons on a unit spatial scale at energy level E, the DOM function energy spectrum M is generated. es (E); This application proposes K es (E) A second mathematical model can be established that reflects the Maxwell-Boltzmann distribution at equilibrium and the effect of applying a drain-source bias voltage on the overall kinetic energy moving to a higher level; further, based on the first mathematical model, the DOM function energy spectrum and the second mathematical model, the physical model formulas of the internal transmittance and the collective kinetic energy spectrum can be obtained.

[0080] Optionally, in one embodiment of this application, the first mathematical model is:

[0081] Γ es (E)=exp(-2γ+Λ(EE cs ) / φ t,es ),

[0082] in, It is derived from the WKB approximation used to describe the tunneling process. q represents Planck's constant, and q represents the elementary charge. Represents the effective electron mass, ρ s Represents the local effective charge density, ∈ s E represents the dielectric constant of a semiconductor. csThe conduction band bottom of the semiconductor channel is represented by E, which represents the electron energy, and Λ(x) represents the ramp function. t,es Represents the electron injection barrier of the injection source junction;

[0083] The DOM function energy spectrum is:

[0084]

[0085] Among them, g v For the sake of simplifying and measuring, K is the effective mass of the source junction electrons. es (E) represents the collective kinetic energy spectrum of the source junction electrons;

[0086] The second mathematical model is:

[0087]

[0088] Among them, E b,es V represents ds The ground state kinetic energy when φ = 0 a,es T represents the source junction electron accelerating barrier. s This represents the source junction temperature.

[0089] In actual implementation, such as Figure 4 As shown, for electrons with energies higher than the conduction band edge (E>E), cs E cs (representing the conduction band bottom at the source-channel interface), embodiments of this application can primarily utilize thermal emission; while for electrons with energies lower than the conduction band edge (E...),... <E cs The main mode of transportation is tunneling, and the corresponding first mathematical model is as follows:

[0090] Γ es (E)=exp(-2γ+Λ(EE cs ) / φ t,es ),

[0091] in, It is derived from the WKB approximation used to describe the tunneling process. q represents Planck's constant, and q represents the elementary charge. Represents the effective electron mass, ρ s Represents the local effective charge density, ∈ s E represents the dielectric constant of a semiconductor. cs The conduction band bottom of the semiconductor channel is represented by E, which represents the electron energy, and Λ(x) represents the ramp function. t,es This represents the electron injection barrier of the injection source junction.

[0092] Where, φ t,esThe electron injection barrier of the injection source junction represents the energy E when the energy E exceeds E0. cs Then, the thermal emission injection mechanism is activated.

[0093] DOM function energy spectrum M es (E) represents the number of collective momentum modes contained in the source junction electrons per unit spatial scale at energy level E, as shown in the following formula:

[0094]

[0095] Among them, g v For the sake of simplifying and measuring, K is the effective mass of the source junction electrons. es (E) represents the collective kinetic energy spectrum of the source junction electrons.

[0096] This application embodiment proposes K es (E) can represent the Maxwell-Boltzmann distribution at equilibrium and reflect the effect of applying drain-source bias voltage to shift the overall kinetic energy to a higher level. Therefore, a second mathematical model is proposed:

[0097]

[0098] Among them, E b,es V represents ds The ground state kinetic energy when φ = 0 a,es T represents the accelerating potential barrier for source junction electrons. s This represents the source junction temperature.

[0099] The embodiments of this application can provide a basis for obtaining the physical model formulas of internal transmittance and collective kinetic energy spectrum based on the first mathematical model, the DOM function energy spectrum and the second mathematical model, thereby further improving the physical reliability and computational efficiency of the model.

[0100] In step S103, based on the coordinate intervals of the source junction, intrinsic channel, and drain junction, and the mathematical model of the established Landauer carrier transport physical picture, the current transport of the source junction, intrinsic channel, and drain junction is generated in the form of the quasi-Fermi level phase space (QFLPS) using the preset Landauer formula and the preset drift diffusion formula, respectively, and the comprehensive formula of the current is obtained.

[0101] Specifically, in this embodiment, the current transport in the source and drain regions can be described using the Landauer formula based on the coordinate ranges of the source junction, intrinsic channel, and drain junction, and the current transport in the intrinsic channel can be described using the drift-diffusion formula, thus obtaining a comprehensive formula for the electronic current, namely the Landauer-QFLPS formula. The drift-diffusion formula in this embodiment can be modeled using the Quasi-Fermi-Level Phase Space (QFLPS) theory.

[0102] This application proposes that the Landauer quantum transport formula at the junction can be organically combined with the QFLPS transport formula at the channel to derive a comprehensive current formula, namely the Landauer-QFLPS formula.

[0103] First, we can define a dimensionless index function A(E):

[0104] Γ es (E)M es (E)=e A(E) [m -1 ],

[0105] To balance the dimensions, a wave vector unit is inserted on the right-hand side of the equation. Therefore, based on the first mathematical model, the DOM function energy spectrum, and the second mathematical model, the piecewise function form of function A(E) can be written as follows:

[0106]

[0107] Using the defined A(E) function, the Landauer formula for source-junction electron transport can be further modified:

[0108]

[0109] Rewrite the Fermi window in the integral as a definite integral of the Fermi-Dirac distribution derivative:

[0110]

[0111] The density of a two-dimensional electron gas is a constant density of states and is proportional to the energy integral of the Fermi-Dirac distribution function.

[0112]

[0113] in, The channel state density of the two-dimensional semiconductor material is given (spin valley degeneracy is set to 1).

[0114] Therefore, conversely, the Fermi-Dirac distribution function f F.D. It can be expressed as the partial derivative of n:

[0115]

[0116] And note a useful identity relation:

[0117]

[0118] In this embodiment, the definite integral form of the rewritten Fermi-Dirac distribution derivative can be substituted into the modified Landauer formula for source-junction electron transport, and the order of inner and outer integration can be swapped to obtain:

[0119]

[0120] Then use the property of the Fermi-Dirac distribution function f F.D. From the relationship with the identities, we can obtain:

[0121]

[0122] Furthermore, by performing a second integration by parts on the inner integral and discarding the boundary terms, we obtain:

[0123]

[0124] Because the index function A(E) is a piecewise linear function, the second derivative A″(E) of the index function A(E) will produce the Dirac impulse function, that is:

[0125]

[0126] Therefore, compared to the Dirac pulse function, the first derivative term of A(E) can be neglected. Using the integral sieving property of the Dirac pulse function, we obtain:

[0127]

[0128] Substituting into the definition of A(E) and then rearranging the constant coefficients, we can obtain a QFLPS-like integral form:

[0129]

[0130] Among them, the approximation n(E) was used. cs E F )≈n(E c E F And define a parameter called the junction effect index:

[0131]

[0132] The QFLPS formula describing intrinsic channel transport is:

[0133]

[0134] The junction current formula in the form of QFLPS is I es Substitute this into the QFLPS formula describing intrinsic channel transport, and note I e =I es Thus, the comprehensive formula for electron current is obtained:

[0135]

[0136] The modeling process in this embodiment can be similarly applied to the drain junction hole current (i.e., the model formulas of the first mathematical model, the DOM function energy spectrum, and the second mathematical model; it should be noted that in this embodiment...) Figure 4 and Figure 5 There is a corresponding hole version, which is dual to the given electronic version (and is easily produced according to industry knowledge, so it will not be discussed further). That is, by establishing a hole version, we can obtain:

[0137]

[0138] Accordingly, the above equation defines the junction effect exponent η of the hole current. hd :

[0139]

[0140] in, φ is the effective mass of the hole. t,d The thermal emission barrier for injecting holes into the drain junction. For the effective quality of the leaky cavity, E b, T represents the ground-state thermal equilibrium kinetic energy of the leaky junction hole. d φ is the equivalent temperature of the leaky junction. sb, Schottky barrier for injecting holes into leaky junctions.

[0141] According to model formula I e and I h It can be seen that η es and η hd Two parameters control the switching of the electron and hole currents predicted by the model between Ohmic and Schottky contact transport characteristics; and the model has a significant speed advantage compared to other models that require solving the internal node voltage.

[0142] It should be noted that the reasoning process in the embodiments of this application has a clear physical meaning and there is no issue of arbitrary weighted averaging.

[0143] In summary, in one embodiment of this application, the mathematical model of the Landauer-QFLPS formula, which integrates the effects of source junction, drain junction, and channel transport characteristics, is as follows:

[0144]

[0145] The limits of integration of the formula are set as follows:

[0146] E Fs =0,

[0147] E Fd =-qV ds ,

[0148] Among them, V gs V represents the gate-source voltage. ds Represents the drain-source voltage, μ n Represents electron mobility, μ p Represents hole mobility, φ′ n Represents the effective electron threshold voltage, φ′ p Represents the effective hole threshold voltage, φ t η represents the channel thermal barrier. es η represents the source-junction electron current limiting index. hd φ represents the drain-hole junction current limiting index. a,es Represents the electron acceleration barrier of the source junction, φ a,hd The hole acceleration barrier represents the junction-hole accelerator; where q represents the elementary charge, W and L represent the channel width and length, respectively, and E... Fn Represents the quasi-Fermi level of electrons, E Fp Represents the hole quasi-Fermi level, E Fs Represents the source-end Fermi level, E Fd Represents the drain-end Fermi level, where n represents the electron concentration and p represents the hole concentration; and n and p are related to E Fn and E Fp The functional relationship is given by the following system of equations;

[0149] q 2 (np) / C ox +Ψ+qV gs =0

[0150]

[0151]

[0152] E Fn =E Fp ,

[0153] Where Ψ represents the electrostatic potential energy of the channel surface (also determined by the self-consistency of the above equation), C ox D represents the surface density of the gate oxide capacitance. e and D h These represent the energy state densities of conduction band electrons and valence band holes, respectively.

[0154] Specifically, the 9 parameters {μ n ,φ′ n ,μ p ,φ′ p ,φ t ,η es ,φ a,es ,η hd ,φ a,hd The remaining parameters, W, L, and C, will be calibrated against experimental data. ox D e and D h There is a clear definition (as a design parameter input for the device, or there are standard values ​​in the literature for reference), so there is no need for calibration.

[0155] The description of the model's ability to run on a circuit simulator states that the current can be represented as a parametric model formula. The non-elementary mathematical operations involved mainly involve two aspects: the integrals contained in the Landauer-QFLPS formula; and the relationship between n and p and E. Fn and E Fp The nonlinear equations represented by the functional relationship can be used to perform the corresponding non-elementary calculations by designing appropriate numerical methods, such as rational fraction approximation and Newton iteration.

[0156] Understandably, in the description of the model's innovation, the key innovation lies in the fact that the current can be expressed as a model formula with parameters. By establishing the physical model formulas for internal transmittance and collective kinetic energy spectrum (and the corresponding hole version not listed here), this application embodiment establishes a model formula for the current to be expressed as a parameterized function. The clear difference from similar formulas reported in the literature lies in the additional precondition factor before integration, which reflects the solution proposed by this application embodiment to the main problem to be solved. That is, the ohmic contact and Schottky contact electrical transport characteristics are continuously connected through this precondition factor. The industry-known parts in a specific field are listed in this application embodiment to maintain the integrity and self-consistency of the model.

[0157] Optionally, in one embodiment of this application, the method further includes: constructing a linearized Gaussian wavelet function over a preset sampling interval to solve a preset optimization problem, and searching a parameter optimization network in parallel to obtain a second-order tensor Y input model for circuit simulation.

[0158] As one possible implementation, embodiments of this application can further propose a model parameter extraction algorithm based on the established model. First, it is assumed that the experimental data... Domain upsampling, where, V represents gs Sampling interval V represents ds Sampling interval.

[0159] The embodiments of this application propose a construction The linearized Gaussian wavelet function H on the x-th surface is defined as:

[0160]

[0161] Where Y is a second-order tensor, Y ij Represents {μ n ,φ′ n ,μ p ,φ p ′,φ t ,η es ,φ a,es ,η hd ,φ a,hd The j-th control parameter of the i-th model parameter in}, h i Represents the coordinates of the control parameter variables derived from the i-th model parameter. The generated piecewise linear function.

[0162] In this application embodiment, X (j) Take as The j-th BW i -Equal division points, therefore BW is required i ≥1.

[0163] Next, solve the following optimization problem:

[0164]

[0165] in, For M g - Divide the intervals equally The b-th division point, For M d - Divide the intervals equally The a-th division point on the [thesis].

[0166] Based on the defined optimization problem, this application proposes a parallel search parameter optimization network, such as... Figure 6 As shown, the parallel search parameter optimization network has the following technical features: First, it considers the search along the BWi configuration dimension; second, it considers the search along the initial value {Y0,σ0} dimension, with the search depths of the BWi configuration and the initial value {Y0,σ0} set to R and Z, respectively. Larger parameters obviously help the optimizer find the global optimum, but also increase computational cost; therefore, the parameters need to be set according to specific circumstances; third, it performs Q-round restart iterations for each seed optimization task in a batch of parallel optimization tasks to ensure that the parameters are fully optimized.

[0167] It should be noted that the optimization problem in this embodiment can be solved offline. The obtained second-order tensor Y can be input into the model and used for circuit simulation. Note that when actually performing the circuit simulation task, it is not necessary to execute the optimization network again.

[0168] The embodiments of this application can extract models from experimentally prepared two-dimensional material field-effect transistors, analyze parameter dispersion, thereby conduct process evaluation, and can be directly applied to model-based circuit simulation.

[0169] Next, we can... Figures 2 to 6 The modeling method for two-dimensional material field-effect transistors according to embodiments of this application will be further described in detail.

[0170] like Figure 2 As shown, the embodiments of this application mainly include three terminals: gate (G), source (S), and drain (D), wherein the current I... ds The transport process is controlled by changing the gate (G) voltage, which flows from the drain (D) through the channel (made of two-dimensional material) into the source (S).

[0171] It should be noted that although the embodiments of this application use a top gate structure for illustrative purposes, the model is not limited to this. For example, it is also applicable to bottom gates or other structures that can be equivalent to the structure shown here.

[0172] First, the channel is divided into three segments: (i) the source junction, (ii) the intrinsic channel, and (iii) the drain junction. For ease of description, the coordinate intervals of the three segments are denoted as [x...]. s ,x si ], [x si ,x di ] and [x di ,x d In this embodiment, (i) the source junction and (iii) the drain junction are described by Landauer formulas for current transport in these two regions, while (ii) the intrinsic channel is described by drift-diffusion formulas for current transport. Specifically, the drift-diffusion formulas in this embodiment can be modeled using the Quasi-Fermi-Level Phase Space (QFLPS) theory. This embodiment establishes a mathematical model of the Landauer carrier transport physical picture of the source junction and drain junction.

[0173] like Figure 3 As shown in the embodiments of this application, the Landauer quantum transport formula at the junction can be organically combined with the QFLPS transport formula at the channel to derive a comprehensive current formula.

[0174] The Landauer equation for source-junction electron transport is as follows:

[0175]

[0176] Where W represents the channel width and q is the elementary charge. To reduce Planck's constant, Γ es (E) is the transmission energy spectrum of electrons injected at the source end, M es (E) represents the mode density energy spectrum (DOM), f F.D. (E,E F ):=(1+exp(EE) F ) / kT) -1 The distribution follows the Fermi-Dirac distribution, where k represents the Boltzmann constant, T represents temperature, and E... Fni E represents the value of the quasi-Fermi level at the intrinsic channel interface. Fpi This is the value of the hole quasi-Fermi level at the intrinsic channel interface.

[0177] This application proposes a transmission energy spectrum Γ es (E) is a mathematical model. Considering the carrier transport mechanism undergoing a transition at the band edge, taking the electron as an example, such as... Figure 4 As shown, for electrons with energies higher than the conduction band edge (E>E), cs E cs The conduction band bottom (representing the source-channel interface) is mainly emitted thermally through the junction; while for electrons with energies lower than the conduction band edge (E... <E cs The main mode of transportation is tunneling, which can be summarized into the following model:

[0178] Γ es (E)=exp(-2γ+Λ(EE cs ) / φ t,es ),

[0179] in, It is derived from the WKB approximation used to describe the tunneling process. q represents Planck's constant, and q represents the elementary charge. Represents the effective electron mass, ρ s Represents the local effective charge density, ∈ s E represents the dielectric constant of a semiconductor. cs The conduction band bottom of the semiconductor channel is represented by E, which represents the electron energy, and Λ(x) represents the ramp function. t,es This represents the electron injection barrier of the injection source junction.

[0180] DOM function energy spectrum M es (E) represents the number of collective momentum modes contained in the source junction electrons per unit spatial scale at the energy level E.

[0181]

[0182] Among them, g v For the sake of simplifying and measuring, K is the effective mass of the source junction electrons. es (E) represents the collective kinetic energy spectrum of the source junction electrons.

[0183] Furthermore, such as Figure 5 As shown, this application proposes K in its embodiments. es (E) It is necessary to represent the Maxwell-Boltzmann distribution at equilibrium and reflect the effect of applying drain-source bias voltage to shift the overall kinetic energy to a higher level. Therefore, the following model is proposed:

[0184]

[0185] Among them, E b,es V represents ds The ground state kinetic energy when φ = 0 a,es T represents the source junction electron accelerating barrier. s This represents the source junction temperature.

[0186] like Figure 6 As shown, this embodiment of the application is a schematic diagram of the model parameter extraction algorithm flow for a modeling method of two-dimensional material field-effect transistors. This embodiment of the application can assume that the experimental data are... Domain upsampling, where, V represents gs Sampling interval V represents ds Sampling interval.

[0187] The embodiments of this application propose a construction The linearized Gaussian wavelet function H on the x-th surface is defined as:

[0188]

[0189] Where Y is a second-order tensor, Y ij Represents {μ n V th,n ,μ p V th,p ,φ t ,η es ,φ a,es ,η hd ,φ a,hd The j-th control parameter of the i-th model parameter in}, h i Represents the coordinates of the control parameter variables derived from the i-th model parameter. The generated piecewise linear function, X (j) Take as The j-th BWi -Equal division points, therefore BW is required i ≥1.

[0190] Next, the embodiments of this application can solve the following optimization problem:

[0191]

[0192] in, For M g - Divide the intervals equally The b-th division point, For M d - Divide the intervals equally The a-th division point on the [thesis].

[0193] Based on the defined optimization problem, embodiments of this application propose a parallel search parameter optimization network, such as... Figure 6 As shown, the parameter optimization network has the following technical features: First, it considers the parameters along BW. i The search is performed along the configuration dimension; secondly, a search along the initial value {Y0,σ0} dimension is considered; BW i The search depths for the configuration and initial values ​​{Y0,σ0} are set to R and Z, respectively. Larger parameters obviously help the optimizer find the global optimum, but they also increase the computational cost. Therefore, these two parameters need to be set according to the specific situation. Third, Q rounds of restart iteration are performed for each seed optimization task in a batch of parallel optimization tasks to ensure that the parameters are fully optimized.

[0194] It should be noted that the optimization problem in this embodiment can be solved offline. The obtained second-order tensor Y can be input into the model for circuit simulation. Note that the optimization network does not need to be executed again when actually performing the circuit simulation task.

[0195] The modeling method for two-dimensional material field-effect transistors (FETs) proposed in this application provides a continuous description of FETs with ohmic and Schottky contacts, along with its corresponding parameter extraction algorithm. Based on this model and algorithm, on the one hand, model extraction can be performed on experimentally fabricated FETs to analyze parameter dispersion and thus conduct process evaluation; on the other hand, it can be directly applied to model-based circuit simulation, improving computational efficiency and meeting the efficiency requirements of power simulation. This solves the problem in related technologies where calculating the final junction-channel series current by solving the internal node voltage using Kirchhoff's current conservation law severely impacts computational efficiency and fails to meet the efficiency requirements of circuit simulation. Furthermore, since the junction and channel essentially interact in series, the method of taking a weighted average in parallel has no physical meaning and is not conducive to evaluating the process from a physical perspective based on experimental results.

[0196] Next, referring to the accompanying drawings, a modeling apparatus for a two-dimensional material field-effect transistor according to an embodiment of this application is described.

[0197] Figure 7 This is a schematic diagram of the structure of a modeling device for a two-dimensional material field-effect transistor according to an embodiment of this application.

[0198] like Figure 7 As shown, the modeling device 10 for the two-dimensional material field-effect transistor includes: a determination module 100, a modeling module 200, and an acquisition module 300.

[0199] Specifically, module 100 is used to determine the bias configuration information for testing the device structure and electrical characteristics of two-dimensional material field-effect transistors, and to determine the coordinate range of the source junction, intrinsic channel and drain junction of the channel.

[0200] Modeling module 200 is used to establish a mathematical model of the Landauer carrier transport physical picture of the source junction and the drain junction based on the coordinate interval of the source junction, intrinsic channel and drain junction.

[0201] The acquisition module 300 is used to generate the current transport of the source junction, intrinsic channel and drain junction in the form of quasi-Fermi level phase space (QFLPS) using the preset Landauer formula and the preset drift diffusion formula, respectively, and obtain the comprehensive formula of the current.

[0202] Optionally, in one embodiment of this application, the modeling module 300 includes: a first establishment unit, a generation unit, a second establishment unit, and an acquisition unit.

[0203] The first establishing unit is used to establish the first mathematical model of the transmission energy spectrum based on the carrier transport mechanism at the energy band edge.

[0204] The generation unit is used to generate the DOM function energy spectrum based on the number of collective momentum modes contained in the source junction electrons per unit spatial scale at a preset energy level.

[0205] The second establishment unit is used to establish a second mathematical model that reflects the Maxwell-Boltzmann distribution at equilibrium and the effect of applying a drain-source bias voltage on the overall kinetic energy moving to a higher level.

[0206] The acquisition unit is used to obtain the physical model formulas of internal transmittance and collective kinetic energy spectrum based on the first mathematical model, the DOM function energy spectrum, and the second mathematical model.

[0207] Optionally, in one embodiment of this application, the first mathematical model is:

[0208] Γ es (E)=exp(-2γ+Λ(EE cs ) / φ t,es ),

[0209] in, It is derived from the WKB approximation used to describe the tunneling process. q represents Planck's constant, and q represents the elementary charge. Represents the effective electron mass, ρ s Represents the local effective charge density, ∈ s E represents the dielectric constant of a semiconductor. cs The conduction band bottom of the semiconductor channel is represented by E, which represents the electron energy, and Λ(x) represents the ramp function. t,es Represents the electron injection barrier of the injection source junction;

[0210] The DOM function energy spectrum is:

[0211]

[0212] Among them, g v For the sake of simplifying and measuring, K is the effective mass of the source junction electrons. es (E) represents the collective kinetic energy spectrum of the source junction electrons;

[0213] The second mathematical model is:

[0214]

[0215] Among them, E b,es V represents ds The ground state kinetic energy when φ = 0 a,es T represents the source junction electron accelerating barrier. s This represents the source-junction temperature. The mathematical model of the Landauer-QFLPS formula is summarized as follows:

[0216]

[0217] The limits of integration of the formula are set as follows:

[0218] E Fs =0,

[0219] E Fd =-qV ds ,

[0220] Among them, V gs V represents the gate-source voltage. ds Represents the drain-source voltage, μ n Represents electron mobility, μ p Represents hole mobility, φ′ n Represents the effective electron threshold voltage, φ′ p Represents the effective hole threshold voltage, φ t η represents the channel thermal barrier. esη represents the source-junction electron current limiting index. hd φ represents the drain-hole junction current limiting index. a,es Represents the electron acceleration barrier of the source junction, φ a,hd The hole acceleration barrier represents the junction-hole accelerator; where q represents the elementary charge, W and L represent the channel width and length, respectively, and E... Fn Represents the quasi-Fermi level of electrons, E Fp Represents the hole quasi-Fermi level, E Fs Represents the source-end Fermi level, E Fd Represents the drain-end Fermi level, where n represents the electron concentration and p represents the hole concentration; and n and p are related to E Fn and E Fp The functional relationship is given by the following system of equations;

[0221] q 2 (np) / C ox +Ψ+qV gs =0

[0222]

[0223]

[0224] E Fn =E Fp ,

[0225] Where Ψ represents the electrostatic potential energy of the channel surface (also determined by the self-consistency of the above equation), C ox D represents the surface density of the gate oxide capacitance. e and D h These represent the energy state densities of conduction band electrons and valence band holes, respectively.

[0226] Optionally, in one embodiment of this application, the modeling device 10 for two-dimensional material field-effect transistors further includes a construction module.

[0227] The construction module is used to construct a linearized Gaussian wavelet function over a preset sampling interval to solve a preset optimization problem, and to search the parameter optimization network in parallel to obtain a second-order tensor Y input model for circuit simulation.

[0228] It should be noted that the explanation of the aforementioned modeling method embodiment for two-dimensional material field-effect transistors also applies to the modeling apparatus for two-dimensional material field-effect transistors in this embodiment, and will not be repeated here.

[0229] The modeling apparatus for two-dimensional material field-effect transistors (FETs) proposed in this application provides a continuous modeling technique for FETs with ohmic and Schottky contacts, along with its corresponding parameter extraction algorithm. Based on this model and algorithm, on the one hand, model extraction can be performed on experimentally fabricated FETs to analyze parameter dispersion and thus conduct process evaluation; on the other hand, it can be directly applied to model-based circuit simulation, improving computational efficiency and meeting the efficiency requirements of power simulation. This solves the problem in related technologies where calculating the final junction-channel series current by solving the internal node voltage using Kirchhoff's current conservation law severely impacts computational efficiency and fails to meet the efficiency requirements of circuit simulation. Furthermore, since the junction and channel essentially interact in series, the method of taking a weighted average in parallel has no physical meaning and is not conducive to evaluating the process from a physical perspective based on experimental results.

[0230] Figure 8 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0231] The memory 801, the processor 802, and the computer program stored on the memory 801 and capable of running on the processor 802.

[0232] When the processor 802 executes the program, it implements the modeling method for two-dimensional material field-effect transistors provided in the above embodiments.

[0233] Furthermore, electronic devices also include:

[0234] Communication interface 803 is used for communication between memory 801 and processor 802.

[0235] The memory 801 is used to store computer programs that can run on the processor 802.

[0236] The memory 801 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0237] If the memory 801, processor 802, and communication interface 803 are implemented independently, then the communication interface 803, memory 801, and processor 802 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be divided into address buses, data buses, control buses, etc. For ease of representation, Figure 8 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0238] Optionally, in a specific implementation, if the memory 801, processor 802, and communication interface 803 are integrated on a single chip, then the memory 801, processor 802, and communication interface 803 can communicate with each other through an internal interface.

[0239] The processor 802 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0240] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described modeling method for two-dimensional material field-effect transistors.

[0241] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0242] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0243] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0244] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0245] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0246] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0247] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0248] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A modeling method for two-dimensional material field-effect transistors, characterized in that, Includes the following steps: Based on the device structure and electrical characteristics test bias configuration information of two-dimensional material field-effect transistors, the coordinate range of the source junction, intrinsic channel and drain junction of the channel is determined. A mathematical model of the Landauer carrier transport physics of the source and drain junctions is established based on the divided coordinate intervals. Based on the coordinate intervals of the source junction, intrinsic channel, and drain junction, and the mathematical model of the established Landauer carrier transport physical picture, the current transport of the source junction, intrinsic channel, and drain junction is generated in the quasi-Fermi level phase space QFLPS form using the preset Landauer formula and the preset drift diffusion formula, respectively, and the comprehensive formula of the current is obtained. The mathematical model for establishing the Landauer carrier transport physical picture of the source junction and drain junction based on the coordinate intervals of the source junction, intrinsic channel, and drain junction includes: establishing a first mathematical model of the transmission energy spectrum based on the carrier transport mechanism at the band edge transition; generating the DOM function energy spectrum based on the number of collective momentum modes contained in the electrons of the source junction per unit spatial scale at a preset energy level; establishing a second mathematical model that reflects the Maxwell-Boltzmann distribution at equilibrium and reflects the effect of applying drain-source bias voltage to move the overall kinetic energy to a higher level; and obtaining the physical model formulas for the internal transmittance and collective kinetic energy spectrum based on the first mathematical model, the DOM function energy spectrum, and the second mathematical model. The first mathematical model is: ， in, It is derived from the WKB approximation used to describe the tunneling process. Represents Planck's constant. Represents the elementary charge. Represents effective electron mass, Represents the local effective charge density, Represents the dielectric constant of a semiconductor. This represents the bottom of the conduction band near the source end of the semiconductor channel. Represents electron energy. Represents the ramp function. Represents the electron injection barrier of the injection source junction; The energy spectrum of the DOM function is: ， wherein, is the valley degeneracy, is the effective mass of the source junction electrons, is the collective kinetic energy spectrum of the source junction electrons; The second mathematical model is: ， wherein, representing ground state kinetic energy at time t, representing source junction electron acceleration potential barrier, representing source junction temperature.

2. The method of claim 1, wherein, The mathematical model for the Landauer-QFLPS formula, which integrates the effects of source junction, drain junction, and channel transport characteristics, is as follows: ， The integration limits of the formula are set as follows: ， in, Represents the gate-source voltage. Represents the drain-source voltage. Represents electron mobility. Represents hole mobility. Represents the effective electron threshold voltage. Represents the effective hole threshold voltage. Represents the thermal barrier of the channel. The source-junction electron junction current limitation index, Represents the hole-drain current limitation index. Represents the source junction electron acceleration barrier, Represents the acceleration barrier of leaky junction holes; among which Represents the elementary charge. and These represent the width and length of the channel, respectively. Represents the quasi-Fermi level of electrons. Represents the quasi-Fermi level of holes. Represents the source-end Fermi level. Represents the drain-end Fermi level. Represents electron concentration. Represents hole concentration; and and and and The functional relationship is given by the following system of equations; in, This represents the electrostatic potential energy of the channel surface (also determined by the self-consistency of the above equation). Represents the surface density of the gate oxide capacitance. and These represent the energy state densities of conduction band electrons and valence band holes, respectively.

3. The method of claim 1, wherein, Also includes: Constructing linearized Gaussian wavelet functions over a pre-set sampling interval to solve a pre-set optimization problem and searching a parameter optimization network in parallel to obtain a second-order tensor for circuit simulation Input model.

4. A modeling apparatus of a two-dimensional material field effect transistor, characterized by, include: The module is used to determine the bias configuration information for testing the device structure and electrical characteristics of two-dimensional material field-effect transistors, and to determine the coordinate range of the source junction, intrinsic channel and drain junction of the channel. The modeling module is used to establish a mathematical model of the Landauer carrier transport physical picture of the source junction and the drain junction based on the coordinate interval of the source junction, intrinsic channel and drain junction. The acquisition module is used to generate the current transport of the source junction, intrinsic channel and drain junction in the quasi-Fermi level phase space QFLPS form using the preset Landauer formula and the preset drift diffusion formula, respectively, and obtain the comprehensive formula of the current. The modeling module includes: a first establishment unit for establishing a first mathematical model of the transmission energy spectrum based on the carrier transport mechanism and the bandgap transition; a generation unit for generating the DOM function energy spectrum based on the number of collective momentum modes contained in the source-junction electrons per unit spatial scale at a preset energy level; a second establishment unit for establishing a second mathematical model that reflects the Maxwell-Boltzmann distribution at equilibrium and reflects the effect of applying a drain-source bias voltage to move the overall kinetic energy to a higher level; and an acquisition unit for obtaining the physical model formulas of the internal transmittance and collective kinetic energy spectrum based on the first mathematical model, the DOM function energy spectrum, and the second mathematical model. The first mathematical model is: ， in, It is derived from the WKB approximation used to describe the tunneling process. Represents Planck's constant. Represents the elementary charge. Represents effective electron mass, Represents the local effective charge density, Represents the dielectric constant of a semiconductor. This represents the bottom of the conduction band near the source end of the semiconductor channel. Represents electron energy. Represents the ramp function. Represents the electron injection barrier of the injection source junction; The energy spectrum of the DOM function is: ， wherein, is the valley degeneracy, is the effective mass of the source junction electron, is the collective kinetic energy spectrum of the source junction electrons; The second mathematical model is: ， in, represent ground state kinetic energy at time Represents the source junction electron acceleration barrier, This represents the source junction temperature.

5. The apparatus of claim 4, wherein, The mathematical model for the Landauer-QFLPS formula, which integrates the effects of source junction, drain junction, and channel transport characteristics, is as follows: ， The integration limits of the formula are set as follows: ， in, Represents the gate-source voltage. Represents the drain-source voltage. Represents electron mobility. Represents hole mobility. Represents the effective electron threshold voltage. Represents the effective hole threshold voltage. Represents the thermal barrier of the channel. The source-junction electron junction current limitation index, Represents the hole-drain current limitation index. Represents the source junction electron acceleration barrier, Represents the acceleration barrier of leaky junction holes; among which Represents the elementary charge. and These represent the width and length of the channel, respectively. Represents the quasi-Fermi level of electrons. Represents the quasi-Fermi level of holes. Represents the source-end Fermi level. Represents the drain-end Fermi level. Represents electron concentration. Represents hole concentration; and and and and The functional relationship is given by the following system of equations; in, This represents the electrostatic potential energy of the channel surface (also determined by the self-consistency of the above equation). Represents the surface density of the gate oxide capacitance. and These represent the energy state densities of conduction band electrons and valence band holes, respectively.

6. The apparatus of claim 4, wherein, Also includes: A construction module is configured to construct a linearized Gaussian wavelet function on a preset sampling interval to solve a preset optimization problem, and to search a parameter optimization network in parallel to obtain a second-order tensor for circuit simulation An input model.

7. An electronic device, comprising: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the modeling method for two-dimensional material field-effect transistors as described in any one of claims 1-3.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the modeling method for two-dimensional material field-effect transistors as described in any one of claims 1-3.

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