A modeling method and modeling device of a carbon nanotube field effect transistor device

Abstract

The application provides a modeling method and a modeling device of a carbon nanotube field effect transistor device, and an equivalent circuit model of the carbon nanotube field effect transistor device is established; the equivalent circuit model comprises a plurality of electrical elements; according to physical structure parameters of the carbon nanotube field effect transistor device, the carbon nanotube field effect transistor device is simulated through a quantum scattering simulation system to obtain electrical characteristics; and the plurality of electrical elements in the equivalent circuit model are optimized according to the electrical characteristics. It can be seen that the carbon nanotube field effect transistor device is simulated by using the quantum scattering simulation system to obtain simulation data reflecting the electrical characteristics, the electrical elements in the equivalent circuit model are optimized according to the physical simulation data, the electrical characteristics of the equivalent circuit model and the carbon nanotube field effect transistor device are more matched, and the accuracy of the equivalent circuit model is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of semiconductor, in particular to a modeling method and a modeling device of a carbon nanotube field effect transistor device. BACKGROUND

[0002] Carbon nanotubes have gradually attracted extensive attention of researchers due to their excellent physical properties. The diameter of a carbon nanotube is only 1-3 nm, which means that the channel of the carbon nanotube as a field effect transistor is more easily controlled by a gate, and therefore, under the same gate capacitance, the potential of the carbon nanotube field effect transistor in equal proportion reduction is greater than that of a traditional silicon-based field effect transistor. The carbon nanotube field effect transistor gradually becomes a replacement material of the traditional silicon-based field effect transistor.

[0003] With the expansion of the scale of integrated circuits and the complication of processes, it is difficult to complete the circuit design of the carbon nanotube field effect transistor by using a manual or experimental method. Therefore, a computer-aided design simulation software must be used, and therefore, a device model in the circuit design is particularly important. Since the carbon nanotube field effect transistor device is relatively novel and is being optimized, there is no very mature device model at present. The existing carbon nanotube field effect transistor device model has problems such as imperfect experimental data, large difference between experimental data, and inability to deeply capture the internal physical properties of the carbon nanotube during modeling, which leads to low accuracy of the model.

[0004] In addition, there is not enough experimental observation data on the quantum tunneling effect and thermal characteristics of the carbon nanotube field effect transistor device, which is also a big difficulty in the current device modeling. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a modeling method and a modeling device of a carbon nanotube field effect transistor device, and to improve the accuracy of the model. The specific solutions are as follows:

[0006] In a first aspect, the present application provides a modeling method of a carbon nanotube field effect transistor device, comprising:

[0007] establishing an equivalent circuit model of the carbon nanotube field effect transistor device; the equivalent circuit model comprises a plurality of electrical elements;

[0008] simulating the carbon nanotube field effect transistor device by using a quantum scattering simulation system according to physical structure parameters of the carbon nanotube field effect transistor device, to obtain electrical characteristics;

[0009] optimizing the plurality of electrical elements in the equivalent circuit model according to the electrical characteristics.

[0010] Optionally, the simulation of the carbon nanotube field effect transistor device by using the quantum scattering simulation system according to the physical structure parameters of the carbon nanotube field effect transistor device to obtain the electrical characteristics comprises:

[0011] obtaining a first charge density according to the physical structure parameters of the carbon nanotube field effect transistor device by using a semi-classical ballistic transport method;

[0012] obtaining a first potential distribution according to the first charge density by using a Poisson equation;

[0013] obtaining a first retarded Green function including a phonon scattering self-energy according to the first potential distribution, so as to obtain a second charge density by using the first retarded Green function; the first retarded Green function satisfies a convergence;

[0014] obtaining a second potential distribution according to the second charge density by using the Poisson equation;

[0015] obtaining an electrical characteristic according to the second charge density and the second potential distribution.

[0016] Optionally, the obtaining a first retarded Green function including a phonon scattering self-energy according to the first potential distribution, so as to obtain a second charge density by using the first retarded Green function, comprises:

[0017] calculating a Hamiltonian and a self-energy matrix according to the first potential distribution, so as to obtain a second retarded Green function; the second retarded Green function does not include the phonon scattering self-energy;

[0018] calculating the phonon scattering self-energy according to the second retarded Green function;

[0019] constructing a third retarded Green function according to the phonon scattering self-energy and the second retarded Green function;

[0020] outputting a third charge density by using the third retarded Green function, adjusting parameters of the third retarded Green function, so as to obtain a first retarded Green function;

[0021] obtaining a second charge density by using the first retarded Green function.

[0022] Optionally, the obtaining a second potential distribution according to the second charge density by using the Poisson equation, comprises:

[0023] obtaining a third potential distribution according to the second charge density by solving the Poisson equation;

[0024] if it is determined that the Poisson equation does not have a convergence by using the third potential distribution, then obtaining a third charge density according to the third potential distribution by using the first retarded Green function;

[0025] obtaining a second potential distribution according to the third charge density by using the Poisson equation.

[0026] Optionally, the electrical characteristics include at least one of the following parameters: current-voltage characteristic curve, energy band curve, electron density spectrum, energy dissipation distribution.

[0027] Optionally, the optimization of the plurality of electrical elements in the equivalent circuit model according to the electrical characteristics includes:

[0028] The plurality of electrical elements in the equivalent circuit model are optimized according to a tunneling current and / or heat dissipation; the tunneling current is determined according to the energy band curve, and the heat dissipation is determined according to an energy current density in the energy dissipation distribution.

[0029] Optionally, the optimization of the plurality of electrical elements in the equivalent circuit model according to the electrical characteristics includes:

[0030] The number, parameters and connection relationship of the plurality of electrical elements in the equivalent circuit model are optimized according to the electrical characteristics.

[0031] Optionally, the physical structure parameters include: carbon nanotube chirality, gate dielectric constant, oxide layer thickness, channel length, source-gate length, doping density, elastic scattering coefficient, inelastic scattering coefficient, phonon energy, drain voltage and gate voltage.

[0032] In a second aspect, the embodiments of the present application further provide a modeling device of a carbon nanotube field effect transistor device, comprising:

[0033] A establishing unit is configured to establish an equivalent circuit model of the carbon nanotube field effect transistor device; the equivalent circuit model includes a plurality of electrical elements;

[0034] A simulation unit is configured to simulate the carbon nanotube field effect transistor device by a quantum scattering simulation system according to physical structure parameters of the carbon nanotube field effect transistor device, to obtain electrical characteristics.

[0035] An optimization unit is configured to optimize the plurality of electrical elements in the equivalent circuit model according to the electrical characteristics.

[0036] Optionally, the simulation unit is configured to:

[0037] According to the physical structure parameters of the carbon nanotube field effect transistor device, a first charge density is obtained by using a semi-classical ballistic transport method.

[0038] A first potential distribution is obtained by a Poisson equation according to the first charge density.

[0039] A first retarded Green function including a phonon scattering self-energy is obtained according to the first potential distribution, to obtain a second charge density by the first retarded Green function; the first retarded Green function satisfies convergence.

[0040] a second potential distribution is obtained by the Poisson equation according to the second charge density;

[0041] an electrical characteristic is obtained according to the second charge density and the second potential distribution.

[0042] The embodiment of the present application provides a modeling method and a modeling device of a carbon nanotube field effect transistor device, an equivalent circuit model of the carbon nanotube field effect transistor device is established; the equivalent circuit model comprises a plurality of electrical elements; the carbon nanotube field effect transistor device is simulated by a quantum scattering simulation system according to physical structure parameters of the carbon nanotube field effect transistor device, and electrical characteristics are obtained; and the plurality of electrical elements in the equivalent circuit model are optimized according to the electrical characteristics. It can be seen that the carbon nanotube field effect transistor device is simulated by the quantum scattering simulation system to obtain simulation data reflecting the electrical characteristics, the electrical elements in the equivalent circuit model are optimized according to the physical simulation data, the electrical characteristics of the equivalent circuit model and the carbon nanotube field effect transistor device are more matched, and the accuracy of the equivalent circuit model is improved. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0044] Figure 1 A flowchart of modeling of a carbon nanotube field effect transistor device provided by the embodiment of the present application is shown;

[0045] Figure 2 A subband energy distribution diagram provided by the embodiment of the present application is shown;

[0046] Figure 3 A channel internal energy dissipation distribution diagram provided by the embodiment of the present application is shown;

[0047] Figure 4 A heat dissipation amount analytical result caused by phonon scattering provided by the embodiment of the present application is shown;

[0048] Figure 5 A flowchart of quantum scattering system simulation provided by the embodiment of the present application is shown;

[0049] Figure 6 A first subband charge density diagram provided by the embodiment of the present application is shown;

[0050] Figure 7A curve diagram of the leakage current changing with the drain voltage provided in the embodiment of the present application is shown.

[0051] Figure 8 A structural block diagram of a modeling device of a carbon nanotube field effect transistor provided in the embodiment of the present application is shown. DETAILED DESCRIPTION

[0052] In order to make the above objectives, features and advantages of the present application more apparent, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0053] In the following description, a large number of specific details are set forth in order to facilitate a thorough understanding of the present application, but the present application can also be implemented in other ways different from those described herein, and those skilled in the art can make similar generalizations without departing from the connotation of the present application, therefore the present application is not limited to the specific embodiments disclosed below.

[0054] As described in the background, since the carbon nanotube field effect transistor is relatively novel and is being optimized, there is no very mature device model at present. The existing carbon nanotube field effect transistor model has problems such as imperfect experimental data, large difference between experimental data, and inability to deeply capture the internal physical characteristics of the carbon nanotube during modeling, resulting in low model accuracy.

[0055] Based on the above technical problems, the embodiment of the present application provides a modeling method and a modeling device of a carbon nanotube field effect transistor, an equivalent circuit model of the carbon nanotube field effect transistor is established; the equivalent circuit model includes a plurality of electrical elements; the carbon nanotube field effect transistor is simulated by a quantum scattering simulation system according to physical structure parameters of the carbon nanotube field effect transistor, to obtain electrical characteristics; and the plurality of electrical elements in the equivalent circuit model are optimized according to the electrical characteristics. As can be seen, the carbon nanotube field effect transistor is simulated by the quantum scattering simulation system to obtain simulation data reflecting the electrical characteristics, and the electrical elements in the equivalent circuit model are optimized according to the physical simulation data, so that the equivalent circuit model is more matched with the electrical characteristics of the carbon nanotube field effect transistor, and the accuracy of the equivalent circuit model is improved.

[0056] In order to facilitate understanding, the modeling method and the modeling device of a carbon nanotube field effect transistor provided in the embodiment of the present application are described in detail below with reference to the accompanying drawings.

[0057] In the embodiments of the present application, the most widely used model in the transistor model is the equivalent circuit model, which describes the effects of each part of the device by using some equivalent electrical elements, so as to intuitively reflect the physical meaning of the device. However, due to the channel length of the carbon nanotube field effect transistor entering the nanometer level, the device size is very small, and the physical meaning of the device is very complex, involving a large number of integral calculations and uncertainty factors, so it is difficult to simply establish an equivalent circuit model based on the physical meaning of the equation. In order to apply the device model in circuit design engineering, the current carbon nanotube device model is a semi-empirical model with a large number of fitting parameters. However, for emerging devices such as single-walled carbon nanotube array field effect transistor devices, there is not enough experimental data to provide modeling at present, and when the experimental data of the devices under the same parameters have large differences, it is not possible to correctly select the experimental data that is more beneficial to modeling due to the lack of understanding of the internal mechanism, resulting in low accuracy of the existing equivalent circuit model. The embodiments of the present application take building a single-walled carbon nanotube array field effect transistor device model under a 32nm technology node as an example for detailed description.

[0058] Reference Figure 1 As shown in FIG. 1, a flowchart of a carbon nanotube field effect transistor device modeling method provided by the embodiments of the present application is shown, which can include the following steps.

[0059] S101, an equivalent circuit model of the carbon nanotube field effect transistor device is established.

[0060] In the embodiments of the present application, an equivalent circuit model of the carbon nanotube field effect transistor device based on the traditional physical method can be established. The equivalent circuit model includes a plurality of electrical elements, which can be capacitors or resistors, and the electrical elements can be connected in series or parallel. It can be understood that the accuracy of the equivalent circuit model is low, and the problems of the model can be analyzed in order to be optimized in subsequent steps.

[0061] S102, the carbon nanotube field effect transistor device is simulated by a quantum scattering simulation system according to the physical structure parameters of the carbon nanotube field effect transistor device, and the electrical characteristics are obtained.

[0062] In the embodiments of the present application, the physical structure parameters of the carbon nanotube field effect transistor device can be input to the quantum scattering simulation system. The physical structure parameters can include: carbon nanotube chirality, gate dielectric constant, oxide layer thickness, channel length, source-gate length, doping density, elastic scattering coefficient, inelastic scattering coefficient, phonon energy, drain voltage and gate voltage. Specifically, the carbon nanotube chirality is (13, 0), the gate dielectric constant is 16, the oxide layer thickness is 2nm, the channel length is 15nm, the source-gate length is 30nm, the doping density is 15e -8, the elastic scattering coefficient is 0.0109 eV 2 , the inelastic scattering coefficient is 0.0158 eV 2 , the phonon energy is 0.062 eV, the drain voltage can be 0-0.4V, and the gate voltage can be-0.2V-0.4V.

[0063] In the embodiment of the present application, the quantum scattering simulation system can simulate according to the input physical structure parameters, and output simulation results. The simulation results can reflect the electrical characteristics of the carbon nanotube field effect transistor device, and the electrical characteristics can include at least one of the following parameters: current-voltage characteristic curve, energy band curve, electron density spectrum, and energy dissipation distribution. By simulating the carbon nanotube field effect transistor device through the quantum scattering simulation system, a large amount of simulation data can be obtained, which makes up for the defect of less experimental data, and can assist in optimizing the equivalent circuit model, so that the equivalent circuit model is more matched with the electrical characteristics of the carbon nanotube field effect transistor device, and the accuracy of the equivalent circuit model is improved.

[0064] In the embodiment of the present application, the quantum scattering simulation system can simulate according to the input physical structure parameters, and output simulation results. The simulation results can reflect the electrical characteristics of the carbon nanotube field effect transistor device, and the electrical characteristics can include at least one of the following parameters: current-voltage characteristic curve, energy band curve, electron density spectrum, and energy dissipation distribution. By simulating the carbon nanotube field effect transistor device through the quantum scattering simulation system, a large amount of simulation data can be obtained, which makes up for the defect of less experimental data, and can assist in optimizing the equivalent circuit model, so that the equivalent circuit model is more matched with the electrical characteristics of the carbon nanotube field effect transistor device, and the accuracy of the equivalent circuit model is improved.

[0065] In the embodiment of the present application, the quantum scattering simulation system can simulate according to the input physical structure parameters, and output simulation results. The simulation results can reflect the electrical characteristics of the carbon nanotube field effect transistor device, and the electrical characteristics can include at least one of the following parameters: current-voltage characteristic curve, energy band curve, electron density spectrum, and energy dissipation distribution. By simulating the carbon nanotube field effect transistor device through the quantum scattering simulation system, a large amount of simulation data can be obtained, which makes up for the defect of less experimental data, and can assist in optimizing the equivalent circuit model, so that the equivalent circuit model is more matched with the electrical characteristics of the carbon nanotube field effect transistor device, and the accuracy of the equivalent circuit model is improved.

[0066] In the embodiments of the present application, for some electrical characteristics of the carbon nanotube field effect transistor device, the existing equivalent circuit model has not taken into account, for example, tunneling current, heat dissipation, etc. In the carbon nanotube field effect transistor device, there is a quantum tunneling effect. When the potential barrier thickness is close to the electron wavelength, the electron can directly pass through the potential barrier by using its wave property. Therefore, the influence of the tunneling current needs to be considered in the equivalent circuit model. In addition, the thermal characteristics inside the device are not clear. The temperature change inside the channel cannot be derived by physical formula at the nanometer scale. Therefore, it is necessary to add a tunneling current module and a thermal resistance module to the equivalent circuit model through physical simulation, such as constructing new electrical elements, changing the parameters of electrical elements, etc.

[0067] Specifically, the plurality of electrical elements in the equivalent circuit model can be optimized according to the tunneling current, wherein the tunneling current can be determined according to the energy band curve. Figure 2 As shown in the sub-band energy distribution diagram provided by the embodiments of the present application, the sub-band energy distribution diagram includes a conduction band bottom energy change curve and a valence band top energy change curve. The tunneling current can be determined according to the energy band curve. For the tunneling effect, the tunneling current can be calculated by the following Landauer formula:

[0068]

[0069] wherein E fs represents the Fermi level of the source end, E fd represents the Fermi level of the drain end, T is the temperature, k B is the Boltzmann constant, h is the Planck constant, T e (E) is the tunneling probability.

[0070] The tunneling probability can be represented as:

[0071]

[0072] wherein t b (E) can be represented as

[0073]

[0074] wherein v F is the Fermi velocity, h is the Planck constant, E g is the bandwidth, E c (x) is the conduction band energy, x i and x0 are the start point and end point of the tunneling respectively.

[0075] E c (x) can be obtained by solving the Laplace equation, and can be simplified as an analytical model, which can be represented as:

[0076] Ec (x) = a1e -x / λ + a2e x / λ -V G +E g / 2 (4)

[0077] where x is the position in the carbon nanotube field effect transistor, λ is the electrostatic length scale, a1, a2 are analytical parameters, E g is the bandwidth, V G is the gate voltage.

[0078] The tunneling current can be divided into direct source-drain tunneling and junction band tunneling, which needs to be extended to the source-drain region in the above equation, and the formula derivation and simplification are carried out for the two cases respectively, and the analytical parameters such as a1, a2 can be obtained by fitting the conduction band bottom energy curve in the formula. Figure 2

[0079] Specifically, the plurality of electrical elements in the equivalent circuit model can also be optimized according to the heat dissipation, and the heat dissipation can be determined according to the energy current density in the energy dissipation distribution.

[0080] Since the temperature change in the device is related to the heat, the temperature change model can be obtained by analyzing the heat dissipation distribution in the device. The temperature change caused by phonon scattering in the device cannot be directly obtained, but it can be derived from the heat diffusion equation. The heat dissipation caused by phonon scattering can be obtained by the energy current density in the channel, which can be expressed by the formula:

[0081]

[0082] where g(x) is the scattering amount, J E (x) is the energy current density.

[0083] Referring to Figure 3 , which is an energy dissipation distribution diagram inside a channel provided by an embodiment of the present application. The horizontal axis represents the length of the channel, and the vertical axis is the energy current density. The energy current density is derived and fitted to obtain a heat dissipation amount linearly related to x, as shown in Figure 4 , which is an analytical result of heat dissipation caused by phonon scattering provided by an embodiment of the present application. The horizontal axis represents the length of the channel, and the vertical axis is the heat dissipation. The heat dissipation is brought into the solution of the heat diffusion equation to obtain the temperature change inside the carbon nanotube field effect transistor device, and it is introduced into the device model.

[0084] ​In the embodiments of the present application, the physical simulation results are combined with formula induction, the simulation data are fitted according to different requirements, the model parameters of the existing modules in the model are extracted to calibrate the modules, and new modules are constructed and added to the model for the physical characteristics that have not been involved in the model but exist in the simulation, so that the physical simulation of the carbon nanotube field effect transistor device, the physical simulation and the experimental data are mutually assisted and supplemented, and the model is more perfect.

[0085] In the embodiments of the present application, the device model finally applied to the circuit design can be verified by using a simulation tool such as HSPICE based on the relationship between the source-drain voltage and the drain current. The device can also be applied to a simple logic circuit such as an inverter to verify the correctness of its function.

[0086] In the embodiments of the present application, S102 can include various implementation manners, one of which can specifically include the following steps.

[0087] S1021, the first charge density can be obtained by using a semi-classical ballistic transport method according to the physical structure parameters of the carbon nanotube field effect transistor device;

[0088] S1022, the first potential distribution is obtained by a Poisson equation according to the first charge density;

[0089] S1023, the first delay Green function including a phonon scattering self-energy is obtained according to the first potential distribution, so as to obtain the second charge density by the first delay Green function; the first delay Green function satisfies the convergence;

[0090] S1024, the second potential distribution is obtained by a Poisson equation according to the second charge density;

[0091] S1025, the electrical characteristics are obtained according to the second charge density and the second potential distribution.

[0092] In the embodiments of the present application, the first charge density, the energy distribution and other physical quantities in the device are obtained by using a semi-classical ballistic transport method, which are used as reference data and initial guess value input of the next quantum transport method; then, a self-consistent iteration method based on a non-equilibrium Green function method is used, elastic and inelastic phonon scattering is introduced, and the internal physical characteristics of the carbon nanotube field effect transistor with specific parameters are simulated by self-consistently solving the Poisson equation and the non-equilibrium Green function with phonon scattering, so as to solve the second charge density, the second potential distribution, the current and the energy distribution in the device, and then the simulation results are output by a quantum scattering simulation system.

[0093] In the embodiment of the present application, S1023 can include: calculating the Hamiltonian and the self-energy matrix according to the first potential distribution to obtain a second retarded Green function; the second retarded Green function does not include the phonon scattering self-energy; then calculating the phonon scattering self-energy according to the second retarded Green function; next, constructing a third retarded Green function according to the phonon scattering self-energy and the second retarded Green function; adjusting the parameters of the third retarded Green function by using the third charge density output by the third retarded Green function to obtain a first retarded Green function; and obtaining a second charge density by the first retarded Green function.

[0094] In the embodiment of the present application, S1024 can include: solving the Poisson equation according to the second charge density to obtain a third potential distribution; next, if it is determined that the Poisson equation does not have convergence by using the third potential distribution, obtaining a third charge density by the first retarded Green function according to the third potential distribution; and then obtaining a second potential distribution by the Poisson equation according to the third charge density.

[0095] In the embodiment of the present application, referring to Figure 5 Fig. 1 is a flow chart of a quantum scattering system simulation provided by the embodiment of the present application, the physical structure parameters of a carbon nanotube field effect transistor device are input, and the first charge density is obtained by using a semi-classical ballistic transport method; the Poisson equation is solved to obtain a first potential distribution, wherein the Poisson equation is specifically:

[0096]

[0097] wherein r represents the coordinate along the diameter direction of the carbon nanotube field effect transistor, z represents the coordinate along the axial direction of the carbon nanotube field effect transistor, p represents the charge density distribution, and ε is the dielectric constant.

[0098] The Hamiltonian and the self-energy matrix are calculated by the first potential distribution to obtain a second retarded Green function. It should be noted that when the retarded Green function is calculated for the first time, the phonon scattering self-energy is not considered. Specifically, the basis set is determined for the independent channel and the Hamiltonian matrix is calculated, the two-dimensional nanotube lattice is transformed into n non-coupled one-dimensional lattices in the mode space, and the transformed Hamiltonian matrix H pz can be represented as

[0099]

[0100] wherein the diagonal elements U i correspond to the field static potential along the tube surface, m represents the mth mode, N represents N lattices, and b 2m = 2tcos(πm / n).

[0101] The self-energy matrix and the self-energy matrix describing how the transport channel is coupled to the source contact and the drain contact can be calculated, and the self-energy matrix ∑(E) can be represented as

[0102] ∑(E) = ∑ S (E) + ∑ D (E) (8)

[0103] where ∑ S (E) represents the self-energy matrix of the source end, ∑ D (E) represents the self-energy matrix of the drain end.

[0104] Then, the second retarded Green function can be expressed as

[0105] G(E) = [(E + iη + )I - H pz - ∑(E)] -1 (9)

[0106]

[0107]

[0108] where G n represents the Green function of electron transport, G p represents the Green function of hole transport, η + represents a very small quantity, E represents energy, I is the unit matrix, H pz is the Hamiltonian matrix, and ∑(E) is the self-energy matrix.

[0109] It can be understood that the first retarded Green function, the second retarded Green function, and the third retarded Green function can all be expressed by formula (9), and the difference lies in the difference in phonon scattering self-energy.

[0110] The last part of the self-energy matrix is calculated by using the second retarded Green function, which is generated by electron-phonon scattering. The definition of the inelastic intraband scattering self-energy function and the out-of-scattering self-energy function from subband m' to m in a ring j is as follows:

[0111]

[0112]

[0113] where D0 represents the coupling constant, n ω represents the number of phonons, is the phonon energy. Because research shows that the real part of the scattering self-energy has little effect on phonon scattering, only the imaginary part of the scattering self-energy matrix needs to be solved, which is as follows:

[0114]

[0115] The third delay Green function is constructed by a phonon scattering self-energy and a second delay Green function, whether the third charge density converges is judged, if not, a new delay Green function is calculated again, if yes, the third charge density is the second charge density, a Poisson equation is solved according to the second charge density, whether the Poisson equation converges is determined by using the third potential distribution, if not, a new delay Green function is determined according to the third potential distribution, until the Poisson equation and the delay Green function are iteratively self-consistent, and the simulation result is output.

[0116] According to the third delay Green function, the charge density of a certain position z j in the mth subband ring j is determined as

[0117]

[0118] In the embodiment of the present application, Figure 6 The first subband charge density graph provided in the embodiment of the present application can be seen, with the increase of the drain voltage V D , the charge density decreases. Figure 7 The drain current-voltage curve graph provided in the embodiment of the present application can be seen, with the increase of the drain voltage, the drain current first increases and then gradually remains unchanged, and it is found that with the increase of the gate voltage, the drain current also increases.

[0119] In the embodiment of the present application, the problems that the existing carbon nanotube field effect transistor device model has imperfect experimental data, large experimental data difference and cannot deeply capture the internal physical characteristics of the carbon nanotube during modeling are solved, the device physical characteristics are simulated at the nanometer scale by using the non-equilibrium Green function self-consistent iteration method, and quantum effects such as tunneling, energy dissipation and phonon scattering are captured. The simulation result is used to extract and optimize the fitting parameters of the existing modules of the device model, and new modules are constructed for the physical characteristics that have not been involved in the model but exist in the simulation, so that the model is more accurate and perfect.

[0120] The embodiment of the present application provides a modeling method of a carbon nanotube field effect transistor device, an equivalent circuit model of the carbon nanotube field effect transistor device is established; the equivalent circuit model comprises a plurality of electrical elements; the carbon nanotube field effect transistor device is simulated by a quantum scattering simulation system according to physical structure parameters of the carbon nanotube field effect transistor device, and electrical characteristics are obtained; the plurality of electrical elements in the equivalent circuit model are optimized according to the electrical characteristics. It can be seen that the quantum scattering simulation system is used to simulate the carbon nanotube field effect transistor device to obtain simulation data reflecting the electrical characteristics, and the electrical elements in the equivalent circuit model are optimized according to the physical simulation data, so that the equivalent circuit model and the electrical characteristics of the carbon nanotube field effect transistor device are more matched, and the accuracy of the equivalent circuit model is improved.

[0121] Based on the modeling method of the carbon nanotube field effect transistor device above, the embodiment of the present application further provides a modeling device, which refers to Figure 8 For the structure block diagram of the modeling device of the carbon nanotube field effect transistor device provided by the embodiment of the present application, the device can include:

[0122] The establishing unit 100 is configured to establish an equivalent circuit model of the carbon nanotube field effect transistor device; the equivalent circuit model includes a plurality of electrical elements;

[0123] The simulation unit 200 is configured to simulate the carbon nanotube field effect transistor device by a quantum scattering simulation system according to the physical structure parameters of the carbon nanotube field effect transistor device, and obtain electrical characteristics;

[0124] The optimization unit 300 is configured to optimize the plurality of electrical elements in the equivalent circuit model according to the electrical characteristics.

[0125] Optionally, the simulation unit is configured to:

[0126] According to the physical structure parameters of the carbon nanotube field effect transistor device, a first charge density is obtained by using a semi-classical ballistic transport method;

[0127] According to the first charge density, a first potential distribution is obtained by a Poisson equation;

[0128] According to the first potential distribution, a first retarded Green function including a phonon scattering self-energy is obtained, so as to obtain a second charge density by the first retarded Green function; the first retarded Green function satisfies convergence;

[0129] According to the second charge density, a second potential distribution is obtained by the Poisson equation;

[0130] According to the second charge density and the second potential distribution, electrical characteristics are obtained.

[0131] The embodiment of the present application provides a modeling device of a carbon nanotube field effect transistor device, an establishing unit is configured to establish an equivalent circuit model of the carbon nanotube field effect transistor device; the equivalent circuit model includes a plurality of electrical elements; a simulation unit is configured to simulate the carbon nanotube field effect transistor device by a quantum scattering simulation system according to the physical structure parameters of the carbon nanotube field effect transistor device, and obtain electrical characteristics; and an optimization unit is configured to optimize the plurality of electrical elements in the equivalent circuit model according to the electrical characteristics. It can be seen that the carbon nanotube field effect transistor device is simulated by using the quantum scattering simulation system to obtain simulation data reflecting the electrical characteristics, and the electrical elements in the equivalent circuit model are optimized according to the physical simulation data, so that the equivalent circuit model is more matched with the electrical characteristics of the carbon nanotube field effect transistor device, and the accuracy of the equivalent circuit model is improved.

[0132] Each of the embodiments in the specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other. Each of the embodiments focuses on the difference from other embodiments. In particular, the device embodiments are described more simply because they are basically similar to the method embodiments, and the relevant parts can be referred to the part of the method embodiments.

[0133] The above is only the preferred embodiment of the present application. Although the present application has been disclosed as above with the preferred embodiment, it is not intended to limit the present application. Any person skilled in the art can make many possible changes and modifications to the technical solution of the present application or modify it into equivalent embodiments with equivalent changes without departing from the scope of the technical solution of the present application by using the disclosed methods and technical contents. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application without departing from the content of the technical solution of the present application shall still fall within the scope of protection of the technical solution of the present application.

Claims

1. A modeling method for carbon nanotube field-effect transistor devices, characterized in that, include: An equivalent circuit model of a carbon nanotube field-effect transistor device is established; the equivalent circuit model includes multiple electrical components. Based on the physical structure parameters of the carbon nanotube field-effect transistor device, the electrical characteristics of the device are obtained by simulating it using a quantum scattering simulation system. Based on the electrical characteristics, multiple electrical components in the equivalent circuit model are optimized; The electrical characteristics of the carbon nanotube field-effect transistor device are obtained by simulating the device using a quantum scattering simulation system based on its physical structure parameters, including: The first charge density is obtained using a semiclassical ballistic transport method based on the physical structure parameters of the carbon nanotube field-effect transistor device. The first potential distribution is obtained from the first charge density using the Poisson equation; A first delayed Green's function, including phonon scattering self-energy, is obtained based on the first potential distribution, and a second charge density is obtained through the first delayed Green's function; the first delayed Green's function satisfies convergence. The second potential distribution is obtained from the second charge density using the Poisson equation; The electrical properties are obtained based on the second charge density and the second potential distribution.

2. The method according to claim 1, characterized in that, The step of obtaining a first delayed Green's function, including phonon scattering self-energy, based on the first potential distribution, and then obtaining a second charge density through the first delayed Green's function, includes: The Hamiltonian and self-energy matrix are calculated based on the first potential distribution to obtain the second delayed Green's function; the second delayed Green's function does not include phonon scattering self-energy. The phonon scattering self-energy is calculated based on the second delayed Green's function; A third delayed Green's function is constructed based on the phonon scattering self-energy and the second delayed Green's function; Using the third charge density output by the third delayed Green's function, the parameters of the third delayed Green's function are adjusted to obtain the first delayed Green's function; The second charge density is obtained through the first delayed Green's function.

3. The method according to claim 2, characterized in that, The step of obtaining the second potential distribution based on the second charge density using the Poisson equation includes: The third potential distribution is obtained by solving the Poisson equation based on the second charge density; If the third potential distribution is used to determine that the Poisson equation does not have convergence, then the third charge density is obtained through the first delayed Green's function based on the third potential distribution. The second potential distribution is obtained from the third charge density using the Poisson equation.

4. The method according to claim 1, characterized in that, The electrical characteristics include at least one of the following parameters: current-voltage characteristic curve, band structure, electron density spectrum, and energy dissipation distribution.

5. The method according to claim 4, characterized in that, The optimization of multiple electrical components in the equivalent circuit model based on the electrical characteristics includes: Based on the tunneling current and / or heat dissipation, multiple electrical components in the equivalent circuit model are optimized; the tunneling current is determined based on the band structure, and the heat dissipation is determined based on the energy current density in the energy dissipation distribution.

6. The method according to claim 1, characterized in that, The optimization of multiple electrical components in the equivalent circuit model based on the electrical characteristics includes: The number, parameters, and connection relationships of multiple electrical components in the equivalent circuit model are optimized based on the electrical characteristics.

7. The method according to any one of claims 1-6, characterized in that, The physical structural parameters include: carbon nanotube chirality, gate dielectric constant, oxide layer thickness, channel length, source-gate length, doping density, elastic scattering coefficient, inelastic scattering coefficient, phonon energy, drain voltage, and gate voltage.

8. A modeling device for carbon nanotube field-effect transistor devices, characterized in that, include: Establish a unit to build the equivalent circuit model of the carbon nanotube field-effect transistor device; The equivalent circuit model includes multiple electrical components; The simulation unit is used to simulate the carbon nanotube field-effect transistor device using a quantum scattering simulation system based on the physical structure parameters of the carbon nanotube field-effect transistor device, and obtain its electrical characteristics. An optimization unit is used to optimize multiple electrical components in the equivalent circuit model based on the electrical characteristics. The simulation unit is used for: The first charge density is obtained using a semiclassical ballistic transport method based on the physical structure parameters of the carbon nanotube field-effect transistor device. The first potential distribution is obtained from the first charge density using the Poisson equation; A first delayed Green's function, including phonon scattering self-energy, is obtained based on the first potential distribution, and a second charge density is obtained through the first delayed Green's function; the first delayed Green's function satisfies convergence. The second potential distribution is obtained from the second charge density using the Poisson equation; The electrical properties are obtained based on the second charge density and the second potential distribution.

Images