Methods, apparatus, and computer equipment for determining the channel mobility of field-effect transistors.

Abstract

This application relates to a method, apparatus, and computer device for determining the channel mobility of a field-effect transistor (FET). The method includes: acquiring a transfer characteristic curve of a target FET; determining a target effective electric field intensity range corresponding to the gate voltage of the target FET based on the transfer characteristic curve; determining the transistor bulk mobility of the target FET based on a bulk mobility model; determining the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET based on the target effective electric field intensity range, using a target Coulomb scattering mobility model, a target phonon scattering mobility model, and a target surface roughness scattering mobility model; and finally determining the channel mobility of the target FET based on a channel mobility model. This approach enables rapid and effective evaluation of device performance, avoids complex analysis and testing, and accelerates the development speed of device processes.

Description

Technical Field

[0001] This application relates to the field of field-effect transistor technology, and in particular to a method, apparatus, and computer device for determining the channel mobility of a field-effect transistor. Background Technology

[0002] Due to its excellent physical properties, silicon carbide is widely used in power devices and integrated circuits. Among them, silicon carbide MOSFETs (metal-oxide semiconductor FETs, field-effect transistors) are a type of device that has attracted much attention. However, due to the poor quality of the gate oxide interface of MOSFETs, the channel mobility of MOSFETs is much lower than expected, thus limiting the overall performance of the device. In research and engineering practice, to characterize the channel mobility, lateral MOSFET devices are usually fabricated, their transfer characteristic curves are tested, and the field-effect mobility is extracted for analysis. However, for in-depth research and to provide guidance for device simulation, a physical model needs to be established. This requires more time-consuming and complex testing and characterization, such as fabricating special Hall device structures, testing electrical parameters under a magnetic field, and different device parameters such as epitaxial doping concentration. It is also necessary to fabricate MOS capacitors. These methods are usually time-consuming, resulting in low efficiency in calculating the channel mobility of field-effect transistors, and high engineering workload and cost, which is not conducive to the iterative upgrading of device process development. At the same time, the established physical models are also more complex. Therefore, improving the computational efficiency of field-effect transistor channel mobility and reducing the computational cost of MOSFET channel mobility are problems that need to be solved. Summary of the Invention

[0003] Therefore, it is necessary to provide a method, apparatus, and computer device for determining the channel mobility of a field-effect transistor (FET) that can improve the computational efficiency of FET channel mobility and reduce the computational cost of MOSFET channel mobility, in order to address the aforementioned technical problems.

[0004] In a first aspect, this application provides a method for determining the channel mobility of an effect transistor, the method comprising:

[0005] A target gate stress is applied to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, the transfer characteristic curve of the target field-effect transistor is obtained.

[0006] Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor;

[0007] The bulk mobility of the target field-effect transistor is determined based on the bulk mobility model.

[0008] Based on the effective electric field intensity range of the target, the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor are determined according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0009] Based on the channel mobility model, the channel mobility of the target field-effect transistor is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor.

[0010] In one embodiment, the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor is determined based on the transfer characteristic curve of the target field-effect transistor, including:

[0011] Determine the depletion layer charge density of the target field-effect transistor based on its transfer characteristic curve.

[0012] Based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the target field-effect transistor, the range of the target effective electric field intensity corresponding to the gate voltage of the target field-effect transistor is determined.

[0013] In one embodiment, the channel mobility model includes: μ = 1 / (1 / μ) b +1 / μ c +1 / μ p +1 / μ sr ); where μ is the channel mobility, μ b μ is the transistor bulk mobility. c Coulomb scattering mobility, μ p μ is the phonon scattering mobility. sr denoted as Surface roughness scattering mobility.

[0014] In one embodiment, the target Coulomb scattering mobility model includes: μ c = A c × E eff αc ;

[0015] Where, μ c Let A be the Coulomb scattering mobility. c E represents the fitting parameters for the Coulomb scattering mobility model. eff αc The first effective electric field intensity interval within the target effective electric field intensity interval;

[0016] The target phonon scattering mobility model includes: μ p = A p × E effαp ;

[0017] Where, μ p Let A be the phonon scattering mobility. p E represents the fitting parameters for the target phonon scattering mobility model. eff αp The second effective electric field intensity interval within the target effective electric field intensity interval;

[0018] The target surface roughness scattering mobility model includes: μ sr = A sr × E eff αsr ;

[0019] Where, μ sr For surface roughness scattering mobility, A sr E represents the fitting parameters for the target surface roughness scattering mobility model. eff αsr The third effective electric field intensity interval within the target effective electric field intensity interval;

[0020] The electric field intensity in the third effective electric field intensity range is greater than that in the second effective electric field intensity range; the electric field intensity in the second effective electric field intensity range is greater than that in the first effective electric field intensity range.

[0021] In one embodiment, the volume mobility model includes: μ b =(μ max (300 / T) η - μ min ) / (1+(N D / N ref ) γ )+ μ min ;

[0022] μ b For volume mobility, μ max μ is the maximum bulk mobility of a field-effect transistor. min N is the minimum bulk mobility of a field-effect transistor. D N represents the effective doping concentration of the field-effect transistor. ref η is the reference doping concentration of the field-effect transistor, γ is the temperature coefficient of the field-effect transistor, T is the concentration coefficient of the field-effect transistor, and T is the operating temperature of the field-effect transistor.

[0023] In one embodiment, the method for determining the channel mobility of the field-effect transistor further includes:

[0024] At least three sets of sample gate stresses were applied to the gate of the sample field-effect transistor to obtain the transfer characteristic curve of the sample field-effect transistor.

[0025] Based on the transfer characteristic curve of the sample field-effect transistor, the sample field-effect mobility of the sample field-effect transistor and the range of effective electric field intensity corresponding to the gate voltage of the sample field-effect transistor are determined.

[0026] Construct initial Coulomb scattering mobility models, initial phonon scattering mobility models, and initial surface roughness scattering mobility models;

[0027] Using a global optimization algorithm, the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model are optimized based on the sample field effect mobility and the effective electric field intensity range of the sample, thereby determining the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0028] In one embodiment, a global optimization algorithm is used to optimize the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model based on the sample field effect mobility and the effective electric field intensity range of the sample, thereby determining the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model, including:

[0029] Using a global optimization algorithm, based on the sample field effect mobility and the effective electric field intensity range of the sample, the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model are optimized to determine the fitting parameters of the target Coulomb scattering mobility model, the fitting parameters of the target surface roughness scattering mobility model, and the parameters to be adjusted of the target phonon scattering mobility model.

[0030] The parameters to be adjusted for the target phonon scattering mobility model determined by the sample field-effect transistor at at least three sample operating temperatures are determined, and the target temperature coefficient is determined;

[0031] The fitting parameters of the target phonon scattering mobility model are determined based on the target temperature coefficient.

[0032] Secondly, this application also provides an apparatus for determining the channel mobility of an effect transistor, the apparatus comprising:

[0033] The transfer characteristic curve determination module is used to apply target gate stress to the gate of the target field-effect transistor for a preset time, and to obtain the transfer characteristic curve of the target field-effect transistor after the target gate stress is applied.

[0034] The effective electric field intensity determination module is used to determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor based on the transfer characteristic curve of the target field-effect transistor.

[0035] The bulk mobility determination module is used to determine the transistor bulk mobility of the target field-effect transistor based on the bulk mobility model.

[0036] The mobility parameter determination module is used to determine the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor based on the target effective electric field intensity range, according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0037] The channel mobility determination module is used to determine the channel mobility of the target field-effect transistor based on the channel mobility model, according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor.

[0038] Thirdly, this application also provides a computer device, the computer device including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the following steps:

[0039] A target gate stress is applied to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, the transfer characteristic curve of the target field-effect transistor is obtained.

[0040] Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor;

[0041] The bulk mobility of the target field-effect transistor is determined based on the bulk mobility model.

[0042] Based on the effective electric field intensity range of the target, the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor are determined according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0043] Based on the channel mobility model, the channel mobility of the target field-effect transistor is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor.

[0044] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0045] A target gate stress is applied to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, the transfer characteristic curve of the target field-effect transistor is obtained.

[0046] Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor;

[0047] The bulk mobility of the target field-effect transistor is determined based on the bulk mobility model.

[0048] Based on the effective electric field intensity range of the target, the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor are determined according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0049] Based on the channel mobility model, the channel mobility of the target field-effect transistor is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor.

[0050] The aforementioned method, apparatus, and computer equipment for determining the channel mobility of field-effect transistors (FETs) involve applying a target gate stress to the gate of the target FET for a preset time, acquiring the transfer characteristic curve of the target FET after the target gate stress application is completed, determining the target effective electric field intensity range corresponding to the gate voltage of the target FET based on the transfer characteristic curve, determining the transistor bulk mobility of the target FET based on the bulk mobility model, determining the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET based on the target effective electric field intensity range, and determining the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET based on the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model, and finally determining the channel mobility of the target FET based on the channel mobility model, the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility. This method solves the problems of low computational efficiency, high engineering workload and cost associated with determining the channel mobility of FETs, which hinders iterative upgrades in device process development. The above scheme determines the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor (FET) through target Coulomb scattering mobility models, target phonon scattering mobility models, and target surface roughness scattering mobility models. Based on the channel mobility model, it determines the channel mobility of the target FET according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility. This can improve the computational efficiency of FET channel mobility, reduce the computational cost of FET channel mobility, and reduce the computational workload of FET channel mobility. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating a method for determining the channel mobility of a field-effect transistor in one embodiment.

[0052] Figure 2 This is a flowchart illustrating a method for determining the channel mobility of a field-effect transistor in another embodiment;

[0053] Figure 3 This is a schematic diagram of the transfer characteristic curve of a sample field-effect transistor at 25°C in one embodiment.

[0054] Figure 4 This is a schematic diagram of the transfer characteristic curve of a sample field-effect transistor at 175°C in one embodiment.

[0055] Figure 5 This is a schematic diagram of the transfer characteristic curve of a sample field-effect transistor at 300°C in one embodiment.

[0056] Figure 6This is a flowchart illustrating a method for determining the fitting parameters of a target phonon scattering mobility model in one embodiment.

[0057] Figure 7 This is a schematic diagram of the transfer characteristic curve of an N-channel MOSFET in one embodiment;

[0058] Figure 8 This is a schematic diagram of the mobility of each component when the operating ambient temperature of the sample field-effect transistor is 25°C in one embodiment.

[0059] Figure 9 This is a schematic diagram of the mobility of each component when the operating ambient temperature of the sample field-effect transistor is 175°C in one embodiment.

[0060] Figure 10 This is a schematic diagram of the mobility of each component when the operating environment temperature of the sample field-effect transistor is 300°C in one embodiment.

[0061] Figure 11 This is a schematic diagram comparing the fitted transfer characteristic curve and the experimental transfer characteristic curve in one embodiment;

[0062] Figure 12 This is a schematic diagram comparing the fitted channel mobility and the experimental channel mobility in one embodiment;

[0063] Figure 13 This is a schematic diagram of the transfer characteristic curves of a P-channel MOSFET under different temperature conditions in one embodiment.

[0064] Figure 14 This is a schematic diagram comparing the fitted field-effect mobility and the experimental field-effect mobility under different temperature conditions in one embodiment.

[0065] Figure 15 This is a schematic diagram of the transfer characteristic curves of an N-channel MOSFET under different temperature conditions in one embodiment;

[0066] Figure 16 This is a schematic diagram comparing the experimental field-effect mobility and the fitted field-effect mobility under different temperature conditions in one embodiment.

[0067] Figure 17 This is a structural block diagram of a device for determining the channel mobility of a field-effect transistor in one embodiment;

[0068] Figure 18 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0070] In one embodiment, such as Figure 1 As shown, a method for determining the channel mobility of an effect transistor is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and further to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0071] S110. Apply target gate stress to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, obtain the transfer characteristic curve of the target field-effect transistor.

[0072] Gate stress refers to the stress exerted on the gate of a semiconductor device under dynamic voltage changes. When the gate voltage of a MOSFET fluctuates dynamically with circuit signals, it causes changes in the charge distribution of the oxide layer, leading to effects such as threshold voltage drift and decreased mobility. The transfer characteristic curve is a core graphical tool for characterizing the performance of a field-effect transistor (FET). It visually demonstrates the control effect of the gate-source voltage on the drain current through the functional relationship between the drain current and the gate-source voltage. The voltage corresponding to the target gate stress can be set according to actual needs. The target FET refers to the MOSFET for which channel mobility calculations are required.

[0073] It should be noted that, taking a silicon carbide MOSFET as an example, the applied target gate stress must not break down the gate dielectric of the target MOSFET to ensure its normal operation.

[0074] Specifically, a target gate stress is applied to the gate of the target MOSFET for a predetermined time. During this stress application, the source and drain of the target MOSFET are kept short-circuited to ensure that the gate dielectric layer withstands the predetermined electric field. Immediately after the target gate stress is applied, the transfer characteristic curve of the target MOSFET is tested. During this process, the voltage between the drain and source of the target MOSFET is kept constant, while only the gate voltage is changed to obtain data on the drain current versus the gate voltage. The transfer characteristic curve of the target MOSFET can be plotted based on this data.

[0075] S120. Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor.

[0076] For example, the method for determining the target effective electric field intensity range includes: determining the depletion layer charge density of the target field-effect transistor based on the transfer characteristic curve of the target field-effect transistor; and determining the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the target field-effect transistor.

[0077] The inversion layer charge density and electric field distribution coefficient of the target field-effect transistor can be obtained from the datasheet of the target MOSFET, based on the MOSFET model.

[0078] Specifically, based on the transfer characteristic curve of the target field-effect transistor, the threshold voltage of the target MOSFET is determined. Based on the known relationship between the threshold voltage and the depletion layer charge density, the depletion layer charge density of the target MOSFET is determined according to its threshold voltage. Based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the target field-effect transistor, the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor is determined. The target effective electric field intensity range can be calculated using formula (1), which is:

[0079] (1)

[0080] in, For the target effective electric field strength, The depletion layer charge density of the target field-effect transistor. The electric field distribution coefficient of the target field-effect transistor is denoted as . The value is 0.33. The inversion layer charge density of the target field-effect transistor.

[0081] The above scheme provides a method for determining the effective electric field intensity range of the target based on the transfer characteristic curve of the target field-effect transistor, which can improve the calculation efficiency of the effective electric field intensity range of the target.

[0082] S130. Determine the transistor bulk mobility of the target field-effect transistor based on the bulk mobility model.

[0083] For example, the volume mobility model includes: μ b =(μ max (300 / T) η - μ min ) / (1+(N D / N ref ) γ )+ μ min ;

[0084] μ b For volume mobility, μ max μ is the maximum bulk mobility of a field-effect transistor. min N is the minimum bulk mobility of a field-effect transistor. D N represents the effective doping concentration of the field-effect transistor. ref Here, η is the reference doping concentration of the field-effect transistor (FET), γ is the temperature coefficient of the FET, γ is the concentration coefficient of the FET, and T is the operating temperature of the FET. The maximum bulk mobility, minimum bulk mobility, effective doping concentration, reference doping concentration, temperature coefficient, and concentration coefficient of the target FET can be obtained from the FET's datasheet.

[0085] For example, when 4H-SiC is used as the material for the target field-effect transistor, the electron mobility μ max =1141cm 2 / Vs, μ min =125cm 2 / Vs. Hole mobility μ max =125cm 2 / Vs, μ min =40cm 2 / Vs.

[0086] Specifically, based on the bulk mobility model, the transistor bulk mobility of the target MOSFET is determined according to the maximum bulk mobility, minimum bulk mobility, effective doping concentration, reference doping concentration, temperature coefficient, concentration coefficient, and operating temperature of the target MOSFET.

[0087] The above scheme provides a way to construct a volume mobility model, which can improve the computational efficiency of volume mobility.

[0088] S140. Based on the effective electric field intensity range of the target, determine the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0089] For example, the target Coulomb scattering mobility model includes: μ c = A c × E eff αc ;

[0090] Where, μ c Let A be the Coulomb scattering mobility. c E represents the fitting parameters for the Coulomb scattering mobility model. eff αc The first effective electric field intensity interval within the target effective electric field intensity interval;

[0091] The target phonon scattering mobility model includes: μ p = A p × E eff αp ;

[0092] Where, μ p Let A be the phonon scattering mobility. p E represents the fitting parameters for the target phonon scattering mobility model. eff αp The second effective electric field intensity interval within the target effective electric field intensity interval;

[0093] The target surface roughness scattering mobility model includes: μ sr = A sr × E eff αsr ;

[0094] Where, μ sr For surface roughness scattering mobility, A sr E represents the fitting parameters for the target surface roughness scattering mobility model. eff αsr The third effective electric field intensity interval within the target effective electric field intensity interval;

[0095] The electric field intensity in the third effective electric field intensity range is greater than that in the second effective electric field intensity range; the electric field intensity in the second effective electric field intensity range is greater than that in the first effective electric field intensity range.

[0096] The first, second, and third effective electric field intensity intervals can be obtained by dividing the target effective electric field intensity interval according to actual needs. For example, the first effective electric field intensity interval can be the range corresponding to the five data points starting from the lowest electric field in the target effective electric field intensity interval. c A p and A sr This can be determined through experiments.

[0097] The above scheme provides a target Coulomb scattering mobility model, a target phonon scattering mobility model, and a target surface roughness scattering mobility model, which can improve the computational efficiency of the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target MOSFET.

[0098] S150. Based on the channel mobility model, the channel mobility of the target field-effect transistor is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor.

[0099] For example, the channel mobility model includes: μ = 1 / (1 / μ) b +1 / μ c +1 / μ p +1 / μ sr );

[0100] Where μ is the channel mobility, μ b μ is the transistor bulk mobility. c Coulomb scattering mobility, μ p μ is the phonon scattering mobility. sr denoted as Surface roughness scattering mobility.

[0101] Understandably, the above scheme solves the problem of the complex physical model established for calculating the channel mobility of field-effect transistors, simplifies the physical model for calculating the channel mobility of field-effect transistors, and improves the calculation efficiency of the channel mobility of field-effect transistors.

[0102] It should be noted that by determining the channel mobility of the target field-effect transistor using the aforementioned channel mobility model, the influence of four mobility parameters—transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility—on the channel mobility of the target field-effect transistor can be determined. For example, based on the transfer characteristic curve of the target field-effect transistor, a set of drain current data as a function of gate voltage can be determined, and therefore the target field-effect mobility of the target field-effect transistor can be calculated based on the transfer characteristic curve. For example, the target field-effect mobility of the target field-effect transistor can be calculated using formula (2), which is:

[0103] (2)

[0104] in, For field-effect mobility, V is the drain current. gs Where L is the gate voltage, W is the channel length of the field-effect transistor, and C is the channel width of the field-effect transistor. oxV is the capacitance per unit area of ​​the oxide layer. ds This is the drain-source voltage.

[0105] Specifically, the channel length, channel width, and oxide capacitance per unit area of ​​the target field-effect transistor (FET) are determined. Based on the transfer characteristic curve of the target FET, the drain current and the corresponding gate voltage are determined. Based on formula (2), the target field-effect mobility of the target FET is determined according to its drain current, corresponding gate voltage, channel length, channel width, and oxide capacitance per unit area. The channel length, channel width, and oxide capacitance per unit area of ​​the target FET can all be obtained from the FET's instruction manual.

[0106] Based on the target field-effect transistor's (FET) target field-effect mobility, transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility, the contributions of these four parameters to the channel mobility of the FET are determined. Based on these four contribution values ​​and the actual requirements for adjusting the channel mobility of the FET, the manufacturing process parameters of the FET are adjusted.

[0107] For example, the formula for calculating the contribution of the transistor bulk mobility to the channel mobility of the target field-effect transistor is shown in formula (3):

[0108] G1= μ FE / μ b (3)

[0109] Wherein, G1 is the contribution of the transistor bulk mobility to the channel mobility of the target field-effect transistor.

[0110] The formula for calculating the contribution of Coulomb scattering mobility to the channel mobility of the target field-effect transistor is shown in formula (4):

[0111] G2=μ FE / μ c (4)

[0112] G2 represents the contribution of Coulomb scattering mobility to the channel mobility of the target field-effect transistor.

[0113] The formula for calculating the contribution of phonon scattering mobility to the channel mobility of the target field-effect transistor is shown in formula (5):

[0114] G3=μ FE / μ p (5)

[0115] Wherein, G3 is the contribution of phonon scattering mobility to the channel mobility of the target field-effect transistor.

[0116] The formula for calculating the contribution of surface roughness scattering mobility to the channel mobility of the target field-effect transistor is shown in formula (6):

[0117] G4=μ FE / μ sr (6)

[0118] Wherein, G4 is the contribution of surface roughness scattering mobility to the channel mobility of the target field-effect transistor.

[0119] For example, if the goal is to adjust the target field-effect transistor (FET) to increase its channel mobility, and the Coulomb scattering mobility has the greatest contribution to the channel mobility, then the fabrication process corresponding to the Coulomb scattering mobility in the target FET can be adjusted. Therefore, by calculating the FET channel mobility using the aforementioned channel mobility model, the direction of process adjustments for the target FET can be determined based on the FET channel mobility calculation process.

[0120] In the aforementioned method for determining the channel mobility of a field-effect transistor (FET), a target gate stress is applied to the gate of the target FET for a preset time. After the target gate stress application is completed, the transfer characteristic curve of the target FET is obtained. Based on the transfer characteristic curve of the target FET, the target effective electric field intensity range corresponding to the gate voltage of the target FET is determined. The transistor bulk mobility of the target FET is determined according to the bulk mobility model. Based on the target effective electric field intensity range, the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET are determined according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model. Based on the channel mobility model, the channel mobility of the target FET is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET. This method solves the problems of low computational efficiency, high engineering workload and cost associated with calculating the channel mobility of FETs, which is detrimental to the iterative upgrading of device process development. The above-described scheme determines the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor (FET) through target Coulomb scattering mobility models, target phonon scattering mobility models, and target surface roughness scattering mobility models. Based on the channel mobility model, it determines the channel mobility of the target FET according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility. This improves the computational efficiency of FET channel mobility calculation, reduces the computational cost of FET channel mobility calculation, and decreases the computational workload of FET channel mobility calculation. Simultaneously, it enables rapid and effective evaluation of device performance, avoids complex analysis and testing, accelerates device process development, speeds up device iterative optimization, and reduces costs.

[0121] In one embodiment, such as Figure 2 As shown, the method for determining the channel mobility of the above-mentioned field-effect transistor also includes:

[0122] S210. Apply at least three sets of sample gate stress to the gate of the sample field-effect transistor and obtain the transfer characteristic curve of the sample field-effect transistor.

[0123] Specifically, at least three sets of sample gate stresses are applied to the gate of the sample field-effect transistor, and at least three sets of transfer characteristic curves of the sample field-effect transistor are obtained.

[0124] For example, if the sample MOSFET is a silicon carbide P-type channel MOSFET, and a voltage is applied to the gate of the sample MOSFET at ambient temperatures of 25°C, 175°C, and 300°C, i.e., sample gate stress is applied, with an applied sample gate stress of -40V, and the thickness of the gate dielectric layer of the sample MOSFET is 50nm, the absolute value of the electric field applied to its gate reaches 8MV / cm. Figure 3 As shown, Figure 3 The data includes transfer characteristic curves of the sample MOSFET without stress and after stress application, with gate voltage applied for durations of 0.1s, 1s, 2s, ..., 10000s. The sample MOSFET operates normally during these stress application periods. The transfer characteristic curves of the sample MOSFET can be tested between the 0.1s and 1s stress application periods. During this process, the drain-source voltage of the sample MOSFET is kept constant at Vds = 0.1V. Then, a gate voltage is applied, with Vgs varying from 0V to -25V in 0.1V steps, thus obtaining a set of transfer characteristic curves for the sample MOSFET.

[0125] It should be noted that the sample gate stress applied to the sample MOSFET and the duration of application can be arbitrarily combined. For example, a 30V gate stress can be applied to the sample MOSFET for 1 second, or a 20V gate stress can be applied for 1 second, or the same gate voltage can be applied to the sample MOSFET as described above, only the application time can be changed. The purpose of applying sample gate stress to the sample MOSFET is solely to change the defect state of the gate dielectric and semiconductor surface of the sample MOSFET, thereby changing the Coulomb scattering mobility parameter of the sample MOSFET. During the acquisition of transfer characteristic data of the sample MOSFET, the drain-source voltage of the sample MOSFET can be selected between 0.02V and 0.1V, the range of the gate voltage of the sample MOSFET is adjusted according to specific MOSFET parameters, and the application step size of the gate voltage of the sample MOSFET can also be adjusted. For example, Figure 4 The transfer characteristic curve of the sample MOSFET was measured when the operating ambient temperature was 175℃. Figure 5 The transfer characteristic curve of the sample MOSFET was measured when the operating ambient temperature was 300℃.

[0126] S220. Based on the transfer characteristic curve of the sample field-effect transistor, determine the sample field-effect mobility of the sample field-effect transistor and the range of effective electric field intensity corresponding to the gate voltage of the sample field-effect transistor.

[0127] Specifically, the channel length, channel width, and oxide capacitance per unit area of ​​the sample field-effect transistor (FET) are determined. Based on the transfer characteristic curve of the sample FET, the drain current and the corresponding gate voltage are determined. Based on formula (2), the sample field-effect mobility of the FET is determined according to the drain current, the corresponding gate voltage, the channel length, the channel width, and the oxide capacitance per unit area.

[0128] Based on the transfer characteristic curve of the sample field-effect transistor, the threshold voltage of the sample MOSFET is determined. Based on the known relationship between the threshold voltage and the depletion layer charge density, the depletion layer charge density of the sample MOSFET is determined according to its threshold voltage. Based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the sample field-effect transistor, the effective electric field intensity range corresponding to the gate voltage of the sample field-effect transistor is determined.

[0129] The effective electric field intensity range of the sample can be calculated using formula (7), which is:

[0130] (7)

[0131] in, The effective electric field intensity range of the sample. The depletion layer charge density of the sample field-effect transistor. The electric field distribution coefficient of the sample field-effect transistor is... It can take the value 0.33. This represents the charge density of the inversion layer of the sample field-effect transistor.

[0132] S230. Construct the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model.

[0133] For example, the initial Coulomb scattering mobility model can be μ_c = A_c×E eff α_c The initial phonon scattering mobility model can be μ_p = A_p × E eff α_p The initial surface roughness scattering mobility model can be μ_sr = A_sr × E eff α_sr Where A_c are the initial parameters of the initial Coulomb scattering mobility model, A_p are the initial parameters of the initial phonon scattering mobility model, and A_sr are the initial parameters of the initial surface roughness scattering mobility model. E eff α_c E represents the first effective electric field intensity interval within the sample's effective electric field intensity interval.eff α_p E represents the second effective electric field intensity interval within the sample's effective electric field intensity interval. eff α_sr This is the third effective electric field intensity interval in the effective electric field intensity interval of the sample.

[0134] S240. Using a global optimization algorithm, based on the sample field effect mobility and the effective electric field intensity range of the sample, the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model are optimized to determine the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0135] The global optimization algorithm can be a genetic algorithm, a simulated annealing algorithm, a particle swarm optimization algorithm, or an ant colony optimization algorithm.

[0136] For example, such as Figure 6 As shown, the method for optimizing the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model to determine the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model includes:

[0137] Using a global optimization algorithm, the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model are optimized based on the sample field-effect mobility and the effective electric field intensity range of the sample. This determines the fitting parameters of the target Coulomb scattering mobility model, the fitting parameters of the target surface roughness scattering mobility model, and the parameters to be adjusted for the target phonon scattering mobility model. Furthermore, the parameters to be adjusted for the target phonon scattering mobility model determined by the sample field-effect transistor at at least three sample operating temperatures are determined, and the target temperature coefficient is identified. Finally, the fitting parameters of the target phonon scattering mobility model are determined based on the target temperature coefficient.

[0138] The above scheme determines the target temperature coefficient based on the parameters to be adjusted in the target phonon scattering mobility model determined by the sample field-effect transistor under different operating ambient temperatures; and determines the fitting parameters of the target phonon scattering mobility model based on the target temperature coefficient, which can improve the accuracy of the fitting parameters of the target phonon scattering mobility model, thereby improving the reliability of the target phonon scattering mobility model.

[0139] For example, based on the above embodiments, the method for determining the channel mobility of an effect transistor includes:

[0140] At least three sets of sample gate stresses were applied to the gate of the sample field-effect transistor to obtain the transfer characteristic curve of the sample field-effect transistor.

[0141] At least three sets of sample gate stresses are applied to the gate of the sample field-effect transistor (FET), and the transfer characteristic curve of the FET is obtained. The channel length, channel width, and oxide capacitance per unit area of ​​the FET are determined. Based on the transfer characteristic curve of the FET, the drain current and the corresponding gate voltage are determined. Based on the drain current, the corresponding gate voltage, channel length, channel width, and oxide capacitance per unit area of ​​the FET, the FET's field-effect mobility is determined. For example, Figure 7 A set of transfer characteristic curves were obtained by testing an N-channel MOSFET after applying stress when the gate voltage was -40V.

[0142] Based on the transfer characteristic curve of the sample field-effect transistor, the threshold voltage of the sample MOSFET is determined. Based on the known relationship between the threshold voltage and the depletion layer charge density, the depletion layer charge density of the sample MOSFET is determined according to its threshold voltage. Based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the sample field-effect transistor, the effective electric field intensity range corresponding to the gate voltage of the sample field-effect transistor is determined.

[0143] We construct initial Coulomb scattering mobility models, initial phonon scattering mobility models, and initial surface roughness scattering mobility models.

[0144] Using a global optimization algorithm, the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model are optimized based on the sample field-effect mobility and the effective electric field intensity range of the sample. This determines the fitting parameters of the target Coulomb scattering mobility model, the fitting parameters of the target surface roughness scattering mobility model, and the parameters to be adjusted for the target phonon scattering mobility model. Furthermore, the parameters to be adjusted for the target phonon scattering mobility model determined by the sample field-effect transistor at at least three sample operating temperatures are determined, and the target temperature coefficient is identified. Finally, the fitting parameters of the target phonon scattering mobility model are determined based on the target temperature coefficient.

[0145] A target gate stress is applied to the gate of the target MOSFET for a predetermined time. During this stress application, the source and drain of the target MOSFET are kept short-circuited to ensure that the gate dielectric layer withstands the predetermined electric field. Immediately after the target gate stress application is completed, the transfer characteristic curve of the target MOSFET is tested. During this process, the voltage between the drain and source of the target MOSFET is kept constant, while only the gate voltage is changed to obtain data on the drain current versus the gate voltage. The transfer characteristic curve of the target MOSFET can be plotted based on this data.

[0146] Based on the transfer characteristic curve of the target field-effect transistor, the threshold voltage of the target MOSFET is determined. Based on the known relationship between the threshold voltage and the depletion layer charge density, the depletion layer charge density of the target MOSFET is determined according to its threshold voltage. Based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the target field-effect transistor, the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor is determined.

[0147] Based on the bulk mobility model, the bulk mobility of the target MOSFET is determined according to the maximum bulk mobility, minimum bulk mobility, effective doping concentration, reference doping concentration, temperature coefficient, concentration coefficient, and operating temperature of the target MOSFET.

[0148] Based on the effective electric field intensity range of the target, the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor are determined according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model. Based on the channel mobility model, the channel mobility of the target field-effect transistor is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility.

[0149] For example, when optimizing the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model, since the Coulomb scattering mobility generally dominates the channel mobility in the low effective electric field region, while the surface roughness scattering mobility dominates the channel mobility in the high effective electric field region, phonon scattering plays a role between the main conductive field ranges of these two scattering mobilities. Therefore, a global optimization algorithm can be used to fit the initial parameters of the initial Coulomb scattering mobility model based on the first effective electric field intensity range within the sample's effective electric field intensity range and the sample's field effect mobility. During this stage, the phonon scattering mobility and the surface roughness scattering mobility remain unchanged. Similarly, based on the second effective electric field intensity range within the sample's effective electric field intensity range and the sample's field effect mobility, the initial parameters of the initial phonon scattering mobility model can be fitted. During this stage, the fitted parameters of the Coulomb scattering mobility model and the surface roughness scattering mobility model remain unchanged. Finally, based on the second effective electric field intensity range within the sample's effective electric field intensity range and the sample's field effect mobility, the initial parameters of the initial surface roughness scattering mobility model can be fitted. During this stage, the fitted parameters of the Coulomb scattering mobility model and the phonon scattering mobility model remain unchanged. Taking a P-channel silicon carbide MOSFET as an example, when the gate dielectric layer thickness is 50nm and the epitaxial doping concentration is 3e16cm-3, the effective intensity of the sample electric field is determined to be below 0.7MV / cm based on the transfer characteristic curve of the sample field-effect transistor. Five data points starting from the lowest electric field are selected to fit the Coulomb scattering mobility parameter. In this stage, the phonon scattering mobility and the surface roughness scattering mobility remain unchanged. Then, the phonon scattering mobility parameter is fitted in addition to the main conductive field of the Coulomb scattering mobility.

[0150] Since Coulomb scattering mobility is affected by interface defects located at the interface between the MOSFET gate dielectric and the semiconductor, these interface defects include interface states and fixed charge defects. For Coulomb scattering mobility, A c It reflects the amount of interface defects, α c This reflects the energy level distribution of the interface defects. For phonon scattering mobility, A p The effect of lattice vibrations on mobility is directly related to the physical properties of the MOSFET material and is generally not related to interface defects. Surface roughness scattering mobility is directly related to the roughness of the MOSFET material, which is affected by the fabrication process but is unrelated to interface defects. By applying gate stress, a dataset was constructed in which phonon scattering mobility remains constant while Coulomb scattering mobility changes. Multiple datasets were used to improve the reliability of the fitting data. The global variable in the fitting process was set as the phonon scattering mobility fitting parameter A. p α pFitting parameters for surface roughness scattering mobility and A sr α sr The local variable is the fitting parameter A for the Coulomb scattering mobility. c α c Finally, the global optimization algorithm performs an overall evaluation and fitting optimization of the fitting parameters for multiple sets of algorithm input data. Specifically, it refers to jointly optimizing the global parameters using multiple sets of algorithm input data to ensure that the fitting of the multiple sets of algorithm input data simultaneously reaches the set error range.

[0151] After determining the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model, a channel mobility model can be constructed based on these models. The channel mobility of the sample MOSFET, determined by the channel mobility model, is then compared with the determined sample field-effect mobility of the sample MOSFET to determine the error in its channel mobility. In the error calculation, the sample field-effect mobility can be used as the actual channel mobility. If the error in the channel mobility of the sample MOSFET is less than 5%, then the channel mobility model meets the requirements.

[0152] For example, Figure 8 This diagram illustrates the bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of a sample field-effect transistor (FET) operating at an ambient temperature of 25°C. At 25°C, when the electric field is below approximately 0.35 MV / cm, the Coulomb scattering mobility is lower than the phonon scattering mobility; above 0.35 MV / cm, phonon scattering dominates. The results show a fitting error within 5%, indicating good fitting accuracy.

[0153] Figure 9 This diagram illustrates the bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of a sample field-effect transistor (FET) at an operating ambient temperature of 175°C. At 175°C, the Coulomb scattering mobility is below 0.27 MV / cm, lower than the phonon scattering mobility, indicating that phonon scattering dominates.

[0154] Figure 10This diagram illustrates the bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of a sample field-effect transistor (FET) operating at an ambient temperature of 300°C. At 300°C, the Coulomb scattering mobility is below 0.25 MV / cm, lower than the phonon scattering mobility. However, above 0.25 MV / cm, phonon scattering dominates. When the electric field exceeds 0.27 MV / cm, both bulk mobility and phonon scattering mobility become limiting factors for hole mobility. It is foreseeable that as the temperature continues to rise, bulk mobility and phonon scattering mobility will limit channel mobility over a larger electric field range, at which point they will become the main limiting factors for MOSFET performance.

[0155] For example, taking a 4H-SiC, N-channel MOSFET as an example, parameter verification is performed using TCAD (Technology Computer-Aided Design, a semiconductor process simulation and device simulation tool). Figure 11 This section compares the experimentally obtained transfer characteristic curves of an N-channel MOSFET with those obtained through fitting at an operating ambient temperature of 300℃. At 300℃, the Coulomb scattering mobility is lower than the phonon scattering mobility above 0.54 MV / cm, and further lower than the surface roughness scattering mobility above 0.66 MV / cm. Phonon scattering and surface roughness scattering mobilities gradually become dominant. When the electric field exceeds 1 MV / cm, the surface roughness scattering mobility, lower than the phonon scattering mobility, begins to dominate the channel electron mobility.

[0156] Table 1 shows the fitting parameters of the target Coulomb scattering mobility model, target phonon scattering mobility model, and target surface roughness scattering mobility model under different temperature conditions, obtained by optimizing the fitting parameters of the initial Coulomb scattering mobility model, initial phonon scattering mobility model, and initial surface roughness scattering mobility model using a global optimization algorithm.

[0157] Table 1

[0158]

[0159] For example, in the modeling method for MOSFET channel mobility, the temperature modeling is performed using fitting data at different temperatures. For a sample P-channel MOSFET, the target temperature coefficient of the fitted phonon scattering mobility is β. p =-0.19. Fitting parameters A of the target phonon scattering mobility model determined based on the target temperature coefficient. p For: A p =15.73 (T / 300)βp E eff αc αc is -0.30. The target phonon scattering mobility model at this time includes: μ p =15.73 (T / 300) βp E eff -0.33 .

[0160] Figure 12 The figure compares the channel mobility of the experimentally obtained sample field-effect transistors with the channel mobility obtained through fitting. The fitted mobility shown in the figure has a high consistency with the experimental mobility, with an error within 5%, thus verifying the accuracy of the model parameter extraction. Figure 13 The transfer characteristic curves of P-channel MOSFETs measured at 25°C, 0°C, -50°C, and -100°C are presented using a Keithley 4200A-SCS parameter analyzer and a Lake Shore cryogenic probe station. Figure 14 The graph shows a comparison between the experimentally obtained field-effect mobility and the fitted field-effect mobility under different temperature conditions. The fitting effect meets expectations. Figure 15 The transfer characteristic curves of the N-channel MOSFET measured in the temperature range of -100°C to 25°C are shown. Figure 16 The results show a comparison between the experimental field-effect mobility and the fitted field-effect mobility of N-channel MOSFETs in the temperature range of -100℃ to 25℃.

[0161] Understandably, the above scheme analyzes the influence of phonon scattering mobility, Coulomb scattering mobility, surface roughness scattering mobility, and bulk mobility on channel carrier mobility, and establishes a mathematical model equation for phonon scattering. The fitting results of Coulomb scattering and surface roughness scattering parameters reflect the quality of the fabrication process and directions for improvement, accelerating process iteration and reducing costs.

[0162] In the aforementioned method for determining the channel mobility of a field-effect transistor (FET), a target gate stress is applied to the gate of the target FET for a preset time. After the target gate stress application is completed, the transfer characteristic curve of the target FET is obtained. Based on the transfer characteristic curve of the target FET, the target effective electric field intensity range corresponding to the gate voltage of the target FET is determined. The transistor bulk mobility of the target FET is determined according to the bulk mobility model. Based on the target effective electric field intensity range, the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET are determined according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model. Based on the channel mobility model, the channel mobility of the target FET is determined according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target FET. This method solves the problems of low computational efficiency, high engineering workload and cost associated with calculating the channel mobility of FETs, which is detrimental to the iterative upgrading of device process development. The above scheme determines the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor (FET) through target Coulomb scattering mobility models, target phonon scattering mobility models, and target surface roughness scattering mobility models. Based on the channel mobility model, it determines the channel mobility of the target FET according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility. This can improve the computational efficiency of FET channel mobility, reduce the computational cost of FET channel mobility, and reduce the computational workload of FET channel mobility.

[0163] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0164] Based on the same inventive concept, this application also provides an apparatus for determining the channel mobility of an effect transistor to implement the method for determining the channel mobility of the effect transistor described above. The solution provided by this apparatus is similar to the solution described in the above method. Therefore, the specific limitations in one or more embodiments of the apparatus for determining the channel mobility of an effect transistor provided below can be found in the limitations of the method for determining the channel mobility of an effect transistor described above, and will not be repeated here.

[0165] In one embodiment, such as Figure 17 As shown, an apparatus for determining the channel mobility of an effect transistor is provided, comprising: a transfer characteristic curve determination module 1701, an effective electric field strength determination module 1702, a bulk mobility determination module 1703, a mobility parameter determination module 1704, and a channel mobility determination module 1705, wherein:

[0166] The transfer characteristic curve determination module 1701 is used to apply a target gate stress for a preset time to the gate of the target field-effect transistor, and to obtain the transfer characteristic curve of the target field-effect transistor after the target gate stress is applied.

[0167] The effective electric field intensity determination module 1702 is used to determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor based on the transfer characteristic curve of the target field-effect transistor.

[0168] The bulk mobility determination module 1703 is used to determine the transistor bulk mobility of the target field-effect transistor based on the bulk mobility model.

[0169] The mobility parameter determination module 1704 is used to determine the Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor based on the target effective electric field intensity range, according to the target Coulomb scattering mobility model, the target phonon scattering mobility model and the target surface roughness scattering mobility model.

[0170] The channel mobility determination module 1705 is used to determine the channel mobility of the target field-effect transistor based on the channel mobility model, according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility of the target field-effect transistor.

[0171] For example, the effective electric field strength determination module 1702 is specifically used for:

[0172] Determine the depletion layer charge density of the target field-effect transistor based on its transfer characteristic curve.

[0173] Based on the depletion layer charge density, inversion layer charge density, and electric field distribution coefficient of the target field-effect transistor, the range of the target effective electric field intensity corresponding to the gate voltage of the target field-effect transistor is determined.

[0174] Furthermore, the channel mobility model includes: μ = 1 / (1 / μ) b +1 / μ c +1 / μ p +1 / μ sr ); where μ is the channel mobility, μ b μ is the transistor bulk mobility. c Coulomb scattering mobility, μ p μ is the phonon scattering mobility. sr denoted as Surface roughness scattering mobility.

[0175] Furthermore, the target Coulomb scattering mobility model includes: μ c = A c ×E eff αc ;

[0176] Where, μ c Let A be the Coulomb scattering mobility. c E represents the fitting parameters for the Coulomb scattering mobility model. eff αc The first effective electric field intensity interval within the target effective electric field intensity interval;

[0177] The target phonon scattering mobility model includes: μ p = A p ×E eff αp ;

[0178] Where, μ p Let A be the phonon scattering mobility. p E represents the fitting parameters for the target phonon scattering mobility model. eff αp The second effective electric field intensity interval within the target effective electric field intensity interval;

[0179] The target surface roughness scattering mobility model includes: μ sr = A sr ×E eff αsr ;

[0180] Where, μ sr For surface roughness scattering mobility, A sr E represents the fitting parameters for the target surface roughness scattering mobility model. eff αsrThe third effective electric field intensity interval within the target effective electric field intensity interval;

[0181] The electric field intensity in the third effective electric field intensity range is greater than that in the second effective electric field intensity range; the electric field intensity in the second effective electric field intensity range is greater than that in the first effective electric field intensity range.

[0182] Furthermore, the volume mobility model includes: μ b =(μ max (300 / T) η - μ min ) / (1+(N D / N ref ) γ )+μ min ;

[0183] μ b For volume mobility, μ max μ is the maximum bulk mobility of a field-effect transistor. min N is the minimum bulk mobility of a field-effect transistor. D N represents the effective doping concentration of the field-effect transistor. ref η is the reference doping concentration of the field-effect transistor, γ is the temperature coefficient of the field-effect transistor, T is the concentration coefficient of the field-effect transistor, and T is the operating temperature of the field-effect transistor.

[0184] For example, the above-mentioned device for determining the channel mobility of the field-effect transistor further includes a mobility model construction module, used for: applying at least three sets of sample gate stresses to the gate of the sample field-effect transistor to obtain the transfer characteristic curve of the sample field-effect transistor; determining the sample field-effect mobility of the sample field-effect transistor and the sample effective electric field intensity range corresponding to the gate voltage of the sample field-effect transistor based on the transfer characteristic curve of the sample field-effect transistor; constructing an initial Coulomb scattering mobility model, an initial phonon scattering mobility model, and an initial surface roughness scattering mobility model; and optimizing the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model based on the sample field-effect mobility and the sample effective electric field intensity range using a global optimization algorithm to determine the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0185] For example, the mobility model building module described above is also used for:

[0186] Using a global optimization algorithm, based on the sample field effect mobility and the effective electric field intensity range of the sample, the fitting parameters of the initial Coulomb scattering mobility model, the initial phonon scattering mobility model, and the initial surface roughness scattering mobility model are optimized to determine the fitting parameters of the target Coulomb scattering mobility model, the fitting parameters of the target surface roughness scattering mobility model, and the parameters to be adjusted of the target phonon scattering mobility model.

[0187] The parameters to be adjusted for the target phonon scattering mobility model determined by the sample field-effect transistor at at least three sample operating temperatures are determined, and the target temperature coefficient is determined;

[0188] The fitting parameters of the target phonon scattering mobility model are determined based on the target temperature coefficient.

[0189] Each module in the aforementioned device for determining the channel mobility of effect transistors can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware within or independently of the processor in a computer device, or stored in software within the memory of the computer device, so that the processor can invoke and execute the operations corresponding to each module.

[0190] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 18 As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When executed by the processor, the computer program implements a method for determining the channel mobility of an effect transistor. The display unit is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0191] Those skilled in the art will understand that Figure 18 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0192] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0193] Step 1: Apply target gate stress to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, obtain the transfer characteristic curve of the target field-effect transistor.

[0194] Step 2: Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor;

[0195] Step 3: Determine the transistor bulk mobility of the target field-effect transistor based on the bulk mobility model;

[0196] Step 4: Based on the effective electric field intensity range of the target, determine the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0197] Step 5: Based on the channel mobility model, determine the channel mobility of the target field-effect transistor according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility.

[0198] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0199] Step 1: Apply target gate stress to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, obtain the transfer characteristic curve of the target field-effect transistor.

[0200] Step 2: Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor;

[0201] Step 3: Determine the transistor bulk mobility of the target field-effect transistor based on the bulk mobility model;

[0202] Step 4: Based on the effective electric field intensity range of the target, determine the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0203] Step 5: Based on the channel mobility model, determine the channel mobility of the target field-effect transistor according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility.

[0204] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, performs the following steps:

[0205] Step 1: Apply target gate stress to the gate of the target field-effect transistor for a preset time. After the target gate stress is applied, obtain the transfer characteristic curve of the target field-effect transistor.

[0206] Step 2: Based on the transfer characteristic curve of the target field-effect transistor, determine the target effective electric field intensity range corresponding to the gate voltage of the target field-effect transistor;

[0207] Step 3: Determine the transistor bulk mobility of the target field-effect transistor based on the bulk mobility model;

[0208] Step 4: Based on the effective electric field intensity range of the target, determine the Coulomb scattering mobility, phonon scattering mobility, and surface roughness scattering mobility of the target field-effect transistor according to the target Coulomb scattering mobility model, the target phonon scattering mobility model, and the target surface roughness scattering mobility model.

[0209] Step 5: Based on the channel mobility model, determine the channel mobility of the target field-effect transistor according to the transistor bulk mobility, Coulomb scattering mobility, phonon scattering mobility and surface roughness scattering mobility.

[0210] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0211] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0212] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0213] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method of determining the channel mobility of a field effect transistor, characterized by, The method comprises the following steps: applying a target gate stress to a gate of a target field effect transistor for a preset time, and obtaining a transfer characteristic curve of the target field effect transistor after the target gate stress is applied; determining a target effective electric field intensity interval corresponding to a gate voltage of the target field effect transistor according to the transfer characteristic curve of the target field effect transistor; determining a transistor body mobility of the target field effect transistor according to a body mobility model; determining a coulomb scattering mobility, a phonon scattering mobility and a surface roughness scattering mobility of the target field effect transistor according to a target coulomb scattering mobility model, a target phonon scattering mobility model and a target surface roughness scattering mobility model based on the target effective electric field intensity interval; determining a channel mobility of the target field effect transistor according to the transistor body mobility, the coulomb scattering mobility, the phonon scattering mobility and the surface roughness scattering mobility of the target field effect transistor based on a channel mobility model; The channel mobility model includes: μ = 1 / (1 / μ b + 1 / μ c + 1 / μ p + 1 / μ sr ) ; wherein, μ is channel mobility, μ b is transistor body mobility, μ c is coulomb scattering mobility, μ p is phonon scattering mobility, μ sr is surface roughness scattering mobility; The target Coulomb scattering mobility model includes: μ c = A c × E eff αc ; wherein μ c is the Coulomb scattering mobility, A c is a fitting parameter of the Coulomb scattering mobility model, E eff αc is a first effective electric field intensity interval in the target effective electric field intensity interval. The target phonon scattering mobility model includes: μ p = A p × E eff αp ; where μ p is the phonon scattering mobility, A p is a fitting parameter of the target phonon scattering mobility model, E eff αp is a second effective electric field intensity interval in the target effective electric field intensity interval. The target surface roughness scattering mobility model includes: μ sr = A sr × E eff αsr ; where μ sr is the surface roughness scattering mobility, A sr is a fitting parameter of the target surface roughness scattering mobility model, E eff αsr is a high third effective electric field intensity interval in the target effective electric field intensity interval. The electric field intensity of the third effective electric field intensity interval is greater than that of the second effective electric field intensity interval, and the electric field intensity of the second effective electric field intensity interval is greater than that of the first effective electric field intensity interval.

2. The method of claim 1, wherein, The method comprises the following steps: determining a depletion layer charge density of the target field effect transistor according to the transfer characteristic curve of the target field effect transistor; determining the target effective electric field intensity interval corresponding to the gate voltage of the target field effect transistor based on the depletion layer charge density, the inversion layer charge density and the electric field distribution coefficient of the target field effect transistor.

3. The method of claim 1, wherein, The volume mobility model includes: μ b =(μ max (300 / T) η - μ min ) / (1+(N D / N ref ) γ )+ μ min ; μ b is the bulk mobility, μ max is the maximum bulk mobility of the field effect transistor, μ min is the minimum bulk mobility of the field effect transistor, N D is the effective doping concentration of the field effect transistor, N ref is the reference doping concentration of the field effect transistor, η is the temperature coefficient of the field effect transistor, γ is the concentration coefficient of the field effect transistor, and T is the operating temperature of the field effect transistor.

4. The method of claim 1, wherein, The method further comprises the following steps: applying at least three groups of sample gate stresses to a gate of a sample field effect transistor, and obtaining a transfer characteristic curve of the sample field effect transistor; determining a sample field effect mobility of the sample field effect transistor, and a sample effective electric field intensity interval corresponding to a gate voltage of the sample field effect transistor according to the transfer characteristic curve of the sample field effect transistor; constructing an initial coulomb scattering mobility model, an initial phonon scattering mobility model and an initial surface roughness scattering mobility model; optimizing fitting parameters of the initial coulomb scattering mobility model, the initial phonon scattering mobility model and the initial surface roughness scattering mobility model according to the sample field effect mobility and the sample effective electric field intensity interval by using a global optimization algorithm, and determining a target coulomb scattering mobility model, a target phonon scattering mobility model and a target surface roughness scattering mobility model.

5. The method of claim 4, wherein, The method of optimizing the fitting parameters of the initial coulomb scattering mobility model, the initial phonon scattering mobility model and the initial surface roughness scattering mobility model according to the sample field effect mobility and the sample effective electric field intensity interval by using a global optimization algorithm, and determining a target coulomb scattering mobility model, a target phonon scattering mobility model and a target surface roughness scattering mobility model comprises the following steps: The fitting parameters of the initial coulomb scattering mobility model, the initial phonon scattering mobility model and the initial surface roughness scattering mobility model are optimized by a global optimization algorithm according to the sample field effect mobility and the sample effective electric field strength interval, fitting parameters of a target coulomb scattering mobility model, fitting parameters of a target surface roughness scattering mobility model and to-be-adjusted parameters of a target phonon scattering mobility model are determined; The to-be-adjusted parameters of the target phonon scattering mobility model determined by the sample field effect transistor at at least three sample working temperatures are determined, and a target temperature coefficient is determined; The fitting parameters of the target phonon scattering mobility model are determined according to the target temperature coefficient.

6. An apparatus for determining the mobility of an effect transistor channel, comprising: The device for determining the channel mobility of the effect transistor comprises: A transfer characteristic curve determination module is configured to apply a target gate stress to a gate of a target field effect transistor for a preset time, and obtain a transfer characteristic curve of the target field effect transistor after the target gate stress is applied; An effective electric field strength determination module is configured to determine a target effective electric field strength interval corresponding to a gate voltage of the target field effect transistor according to the transfer characteristic curve of the target field effect transistor; A bulk mobility determination module is configured to determine a transistor bulk mobility of the target field effect transistor according to a bulk mobility model; A mobility parameter determination module is configured to determine a coulomb scattering mobility, a phonon scattering mobility and a surface roughness scattering mobility of the target field effect transistor according to a target coulomb scattering mobility model, a target phonon scattering mobility model and a target surface roughness scattering mobility model based on the target effective electric field strength interval; A channel mobility determination module is configured to determine a channel mobility of the target field effect transistor according to the transistor bulk mobility, the coulomb scattering mobility, the phonon scattering mobility and the surface roughness scattering mobility of the target field effect transistor based on a channel mobility model. The channel mobility model includes: μ = 1 / (1 / μ b + 1 / μ c + 1 / μ p + 1 / μ sr ) ; wherein, μ is a channel mobility, μ b is a transistor body mobility, μ c is a coulomb scattering mobility, μ p is a phonon scattering mobility, and μ sr is a surface roughness scattering mobility; the target coulomb scattering mobility model includes: μ c = A c × E eff αc ; wherein, μ c is a coulomb scattering mobility, A c is a fitting parameter of the coulomb scattering mobility model, and E eff αc is a first effective electric field intensity interval in a target effective electric field intensity interval; the target phonon scattering mobility model includes: μ p = A p × E eff αp ; wherein, μ p is a phonon scattering mobility, A p is a fitting parameter of the target phonon scattering mobility model, and E eff αp is a second effective electric field intensity interval in the target effective electric field intensity interval; the target surface roughness scattering mobility model includes: μ sr = A sr × E eff αsr ; wherein, μ sr is a surface roughness scattering mobility, A sr is a fitting parameter of the target surface roughness scattering mobility model, and E eff αsr is a third effective electric field intensity interval in the target effective electric field intensity interval; an electric field intensity of the third effective electric field intensity interval is greater than an electric field intensity of the second effective electric field intensity interval; the electric field intensity of the second effective electric field intensity interval is greater than an electric field intensity of the first effective electric field intensity interval. 7.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-6 when the computer program is executed by the processor. The processor executes the computer program to realize the steps of the method of any one of claims 1 to 5.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method of any one of claims 1 to 5.

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