Device interface state density and distribution extraction method, device and equipment

Abstract

The invention discloses a device interface state density and distribution extraction method, device and equipment, relates to the technical field of semiconductor device interface state characterization, and is used for solving the problems of insufficient precision and insufficient spatial analysis capability in the existing interface state characterization method. Comprising the following steps: establishing a physical model representing intrinsic electrical behaviors of a device, performing calibration to obtain a reference model, and determining carrier transport characteristic parameters; based on the reference model, analyzing the carrier mobility change caused by the interface state as a coulomb scattering center, and determining the density of the interface state; a transistor channel is equivalently discretized into a plurality of ballistic transmission units in the spatial dimension, and the non-uniform spatial distribution characteristic of an interface state in the channel is quantitatively represented according to carrier transport characteristic parameters and interface state density. According to the technical scheme provided by the invention, the density of the interface state can be accurately quantified, the spatial distribution of the interface state can be represented, and the accuracy and comprehensiveness of interface state representation are improved.

Description

A method, apparatus and equipment for extracting the interface state density and distribution of a device. Technical Field

[0001] This invention relates to the field of semiconductor device interface state characterization technology, and in particular to a method, apparatus and equipment for extracting device interface state density and distribution. Background Technology

[0002] In the field of semiconductor device reliability characterization, the accurate extraction of interface state density and its spatial distribution is crucial for evaluating device performance and predicting lifetime. However, while device size continues to shrink, the supply voltage has not decreased accordingly, making hot carrier injection (HCI) increasingly prominent and one of the most significant reliability challenges for MOSFET devices. Hot carrier effects lead to the generation of interface states, causing drift in device parameters (such as threshold voltage and transconductance), and the spatial distribution of these defects in the device channel exhibits significant non-uniformity.

[0003] It is worth noting that advanced device structures generally lack traditional body leads. This structural characteristic makes it impossible to directly apply traditional charge pump techniques to these devices for measuring interface state density. Meanwhile, while the commonly used ΔId-Vd test method based on leakage current variations can reflect the spatial distribution of degradation to some extent, it is difficult to quantitatively analyze the non-uniform distribution characteristics of defects within the channel.

[0004] Therefore, given the measurement limitations imposed by advanced device structures, there is an urgent need to develop a more reliable scheme for extracting device interface state density and distribution, in order to achieve quantitative analysis of the interface states and their non-uniform spatial distribution caused by hot carrier degradation. This is crucial for accurately assessing and predicting the long-term reliability and lifetime of devices at advanced process nodes. Summary of the Invention

[0005] The purpose of this invention is to provide a method, apparatus, and device for extracting the density and distribution of device interfaces, in order to solve the problems of insufficient accuracy and lack of spatial resolution in existing interface state characterization methods.

[0006] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for extracting the interface state density and distribution of a device, the method comprising: establishing a physical model characterizing the intrinsic electrical behavior of the device; calibrating the physical model to obtain a reference model; and determining carrier transport characteristic parameters; based on the reference model, analyzing the carrier mobility change caused by the interface state as a Coulomb scattering center, and determining the interface state density; equivalently discretizing the transistor channel in the spatial dimension into multiple ballistic transport units, and quantitatively characterizing the non-uniform spatial distribution characteristics of the interface state in the channel according to the carrier transport characteristic parameters and the interface state density.

[0007] Optionally, a physical model characterizing the intrinsic electrical behavior of the device is established, the physical model is calibrated to obtain a reference model, and carrier transport characteristic parameters are determined, including: characterizing the electrical behavior of the target-size device using the sEKV model; the sEKV model uses the Lambert-W function to establish the relationship between the gate-source voltage and the normalized charge; the Lambert-W function is expressed as: ;in, Represents normalized charge. The lambbert-w function, a product logarithmic function, is defined as f(w) = w·e w inverse function, V represents the gate-source voltage, VTH represents the threshold voltage, DIBL represents the drain-induced barrier reduction factor, and NIDE represents the ideality factor. D Indicates the drain voltage. Representing thermal voltage; calibrating key model parameters; the key model parameters include at least one of threshold voltage, leakage-induced barrier reduction effect factor, and ideality factor; using the formula: Extract the transverse carrier density from the carrier transport characteristic parameters; where, Represents the transverse carrier density. Represents the coefficient. Indicates the inversion coefficient. Indicates horizontal position. Indicates the effective length of the channel.

[0008] Optionally, based on the benchmark model, the carrier mobility change caused by interface states as Coulomb scattering centers is analyzed to determine the interface state density, including: analyzing the influence trend of hot carrier-induced interface states on carrier mobility by monitoring changes in device transconductance; analyzing the carrier mobility reduction effect caused by interface states as Coulomb scattering centers based on the influence trend; and using the formula based on the mobility reduction effect: ; Calculate the actual migration rate; where, This represents the mobility of the Coulomb scattering-confined region when considering interface states. This represents the mobility of the Coulomb scattering-confined region when the interface states are zero. Represents the density of interface states. The reference interface state density is represented; the interface state density is indirectly quantized based on the actual mobility.

[0009] Optionally, the transistor channel is spatially discretized into multiple ballistic transport units, and the non-uniform spatial distribution characteristics of the interface states within the channel are quantitatively characterized based on the carrier transport characteristic parameters and the interface state density. This includes: equating the drift-diffusion transistor to a series of ballistic transistor chains; representing the local degradation caused by the hot carriers as the degradation of carrier velocity and carrier density in each ballistic transport unit; and integrating the degradation of carrier velocity and carrier density in all ballistic transport units through a perturbation sensitivity model to construct an interface state spatial distribution model and analyze the spatial distribution of the interface states.

[0010] Optionally, the degradation of the carrier velocity is converted into an equivalent local mobility field product representation: ;in, This represents the carrier velocity of the Nth ballistic transport unit. Represents the local mobility field product. Indicates the carrier saturation velocity. This represents a coefficient that reflects the velocity saturation effect caused by the electric field.

[0011] Optionally, the degradation of the carrier density is captured by local threshold voltage shift and local ideality factor shift caused by interface states: ; ; ;in, This represents the threshold voltage considering interface state deterioration. This represents the ideal factor that considers the deterioration of the interface state. Indicates oxide layer capacitance. This represents the carrier concentration of the Nth ballistic transport unit. This represents the gate voltage associated with the mapping position based on the original carrier density distribution of each ballistic transistor.

[0012] Optionally, the disturbance sensitivity model is expressed as: ;in, Indicates drain current. Indicates the gate width. The total number of ballistic transmission units. This represents the carrier surface density of the Nth ballistic transport unit. This represents the carrier drift velocity of the Nth ballistic transport unit.

[0013] Compared with existing technologies, this invention provides a method for extracting the interface state density and distribution of a device. It establishes a physical model characterizing the intrinsic electrical behavior of the device and calibrates a benchmark model to determine carrier transport parameters. Based on the benchmark model, it analyzes the carrier mobility variation caused by interface states as Coulomb scattering centers to determine the interface state density. The transistor channel is spatially discretized into multiple ballistic transport units, and the non-uniform spatial distribution characteristics of the interface states within the channel are quantitatively characterized based on the carrier transport parameters and the interface state density. The technical solution provided by this invention ensures the accuracy of the model in its undegraded state through the construction of the benchmark model; by considering the influence of interface states as Coulomb scattering centers, it enables precise quantification of the interface state density; and by converting the channel into multiple ballistic transport units, it effectively analyzes the non-uniform spatial distribution characteristics of the interface states. Therefore, this invention can accurately quantify the interface state density and characterize its spatial distribution, improving the accuracy and comprehensiveness of the interface state characterization.

[0014] In a second aspect, the present invention provides a device for extracting the interface state density and distribution of a device. The device is applied to the device interface state density and distribution extraction method described in the first aspect. The device includes: a model building and calibration module configured to establish a physical model characterizing the intrinsic electrical behavior of the device, calibrate the physical model to obtain a reference model, and determine carrier transport characteristic parameters; an interface state density determination module configured to analyze the carrier mobility change caused by the interface state as a Coulomb scattering center based on the reference model, and determine the interface state density; and a defect spatial distribution extraction module configured to equivalently discretize the transistor channel into multiple ballistic transport units in the spatial dimension, and quantitatively characterize the non-uniform spatial distribution characteristics of the interface state in the channel according to the carrier transport characteristic parameters and the interface state density.

[0015] Thirdly, the present invention provides a device for extracting device interface state density and distribution, the device comprising: a memory, a processor, and a communication interface coupled to the processor; the memory stores a computer program that can be run by the processor; when the processor runs the computer program, it executes the above-described device interface state density and distribution extraction method.

[0016] Fourthly, the present invention provides a computer storage medium storing instructions that, when executed, implement the above-described method for extracting the device interface state density and distribution.

[0017] The technical effects achieved by the device-type solution provided in the second aspect, the equipment-type solution provided in the third aspect, and the computer storage medium solution provided in the fourth aspect are the same as those achieved by the method-type solution provided in the first aspect, and will not be repeated here. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of the invention and constitute a part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 is a flowchart of a device interface state density and distribution extraction method provided by the present invention; Figure 2 is a complete framework schematic diagram of a device interface state density and distribution extraction method provided by the present invention; Figure 3 is a schematic diagram of the channel slicing concept in a device interface state density and distribution extraction method provided by the present invention; Figure 4 is a structural schematic diagram of a device interface state density and distribution extraction device provided by the present invention; Figure 5 is a structural schematic diagram of a device interface state density and distribution extraction equipment provided by the present invention. Detailed Implementation

[0019] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0020] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0021] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0022] Existing technologies typically employ electrical measurement-based methods to estimate interface state density; however, these methods have significant limitations. First, traditional methods struggle to accurately quantify the impact of interface states as Coulomb scattering centers on carrier mobility, leading to inaccurate analyses of carrier transport degradation caused by interface states. Second, existing technologies lack effective spatial resolution capabilities, failing to characterize the non-uniform distribution of interface states within transistor channels. Particularly when analyzing hot carrier-induced interface states, the accuracy of characterization results is limited due to neglecting the local effects of Coulomb scattering and the lack of effective analytical methods for the spatial distribution of defects within the channel. These technical limitations restrict the accuracy and refinement of semiconductor device reliability assessment. Therefore, this invention proposes a device interface state density and distribution extraction scheme combining modeling techniques, capable of accurately quantifying interface state density and characterizing its spatial distribution. Specifically, this invention combines modeling techniques to directly extract and quantify the interface state density during hot carrier degradation, while simultaneously providing in-depth analysis of the non-uniform spatial distribution characteristics of interface states along the device channel direction, thereby providing accurate defect distribution information to support performance evaluation and reliability prediction of devices at advanced process nodes. With devices becoming increasingly miniaturized and structurally complex, this characterization method is expected to quantify the generation and spatial distribution of interface states, providing a key basis for constructing a high-precision hot carrier degradation model, while significantly improving the accuracy of long-term reliability and lifetime prediction for advanced structural devices.

[0023] Next, the solution provided in the embodiments of this specification will be described with reference to the accompanying drawings: In view of the bottleneck problem of the failure of traditional interface state density measurement methods in fully depleted structure devices (such as FDSOI, FinFET), the present invention proposes the method shown in Figure 1. The process may include the following steps: Step 110: Establish a physical model characterizing the intrinsic electrical behavior of the device, calibrate the physical model to obtain a reference model, and determine the carrier transport characteristic parameters.

[0024] Step 110 pertains to basic modeling and calibration. The established model is based on physical principles, such as the statistical distribution of charge carriers and the interaction between electric fields and charge carriers in semiconductor physics, to characterize the electrical response of the device under different operating conditions, such as current-voltage characteristics and capacitance-voltage characteristics. For example, for a metal-oxide-semiconductor field-effect transistor (MOSFET), the physical model considers how the gate voltage controls the concentration of charge carriers in the channel, and how the source-drain voltage drives the movement of charge carriers in the channel to generate current. Since there may be discrepancies between the theoretical model and the actual device, the model needs to be calibrated using experimental data. The calibration process typically involves comparing the model calculation results with the actual measured electrical characteristic data of the device, adjusting parameters in the model (such as carrier mobility and dielectric constant) to ensure that the error between the model calculation results and the experimental data is within an acceptable range.

[0025] After calibration, the resulting model can accurately reflect the intrinsic electrical behavior of the actual device. This verified and adjusted model can be called the baseline model. This step establishes a physical model characterizing the intrinsic electrical behavior of the device, providing a calibrated baseline model and carrier transport characteristic parameters for subsequent analysis, thus forming the physical basis of the entire methodology.

[0026] The process of establishing and calibrating the model involves some parameters related to carrier transport, such as carrier mobility and diffusion coefficient. These parameters describe the movement of carriers in the device. For example, mobility reflects the relationship between the average drift velocity of carriers under the action of an electric field and the electric field strength. Through the model calibration process, the values ​​of these carrier transport characteristic parameters can be accurately determined. These parameters are crucial for understanding the working mechanism and performance of the device.

[0027] Step 120: Based on the benchmark model, analyze the carrier mobility change caused by the interface states as Coulomb scattering centers, and determine the interface state density.

[0028] Interface states are local energy levels located at interfaces (such as semiconductor-oxide interfaces) in semiconductor devices and can serve as Coulomb scattering centers. When charge carriers move in a channel, they interact with these interface states, causing changes in the direction and velocity of the carriers, thus affecting their mobility. Based on established benchmark models, the specific effects of interface states on carrier mobility under different conditions (such as different interface state distributions and different electric field strengths) can be simulated and analyzed. For example, model calculations can reveal how carrier mobility changes with the increase in the number of interface states.

[0029] Interface state density refers to the number of interface states per unit area of ​​an interface. By analyzing changes in carrier mobility and combining known carrier transport theories and models, the interface state density can be deduced. For example, if a quantitative relationship exists between carrier mobility and interface state density, the interface state density can be calculated using measured data on changes in carrier mobility.

[0030] Step 130: The transistor channel is spatially discretized into multiple ballistic transport units, and the non-uniform spatial distribution characteristics of the interface states in the channel are quantitatively characterized according to the carrier transport characteristic parameters and the interface state density.

[0031] Ballistic transport describes the phenomenon where charge carriers, transported in a device channel, move freely from one electrode to another with minimal scattering from lattice vibrations (phonons) and other charge carriers. Discretizing the transistor channel spatially into multiple ballistic transport units allows for more precise analysis of charge carrier transport behavior within the channel. Each ballistic transport unit can be considered a relatively independent region where charge carrier transport approximately satisfies ballistic transport conditions. By discretizing the channel, complex continuous problems can be transformed into a series of discrete, relatively simple problems, facilitating numerical computation and analysis.

[0032] Given the carrier transport characteristics and interface state density, and using a discretized ballistic transport unit model, the spatial distribution of interface states within the channel can be analyzed. Since the distribution of interface states within the channel in actual devices is often non-uniform, the interface state density may differ at different locations, which will have varying impacts on carrier mobility at different positions. By considering the carrier transport within each ballistic transport unit and the role of interface states, the non-uniform spatial distribution characteristics of interface states within the channel can be quantitatively described, such as obtaining information on the numerical values ​​and distribution patterns of the interface state density at different locations.

[0033] The method shown in Figure 1 establishes a physical model characterizing the intrinsic electrical behavior of the device and calibrates it to obtain a benchmark model, thereby determining the carrier transport characteristic parameters. Based on the benchmark model, it analyzes the carrier mobility variation caused by the interface states acting as Coulomb scattering centers, determining the interface state density. The transistor channel is spatially discretized into multiple ballistic transport units, and the non-uniform spatial distribution characteristics of the interface states within the channel are quantitatively characterized based on the carrier transport characteristic parameters and the interface state density. The technical solution provided by this invention ensures the accuracy of the model in its undegraded state through the construction of the benchmark model; by considering the influence of the interface states as Coulomb scattering centers, it enables precise quantification of the interface state density; and by treating the channel as multiple ballistic transport units, it effectively analyzes the non-uniform spatial distribution characteristics of the interface states. Therefore, this invention can accurately quantify the interface state density and characterize its spatial distribution, improving the accuracy and comprehensiveness of the interface state characterization.

[0034] Based on the method in Figure 1, this specification also provides some specific implementation methods of the method, which will be described below.

[0035] This invention establishes the local transport characteristics under the influence of Coulomb scattering, and achieves quantitative analysis of the interface states on carrier transport by correcting the Coulomb scattering mobility and local threshold voltage. Secondly, the transistor channel is equivalent to multiple ballistic transport units ("channel slices"), and the spatial distribution of interface states is analyzed by combining the spatial distribution model of carrier density and velocity. Specifically, as one embodiment of this invention, as shown in Figure 2, the complete implementation process of this invention includes: (1) Basic modeling and calibration: This may include establishing an electrical behavior description based on the sEKV model, calibrating key parameters, and extracting the transverse carrier density distribution. Among them, establishing an electrical behavior description based on the sEKV model: using sEKV (surface potential-based compact model) to construct a mathematical model of the electrical behavior of the device. The mathematical relationship between the gate-source voltage (Vgs) and the interface charge density (qs) is established using the Lambert-W function to describe the gate control characteristics.

[0036] Calibrate key parameters: Use experimental data or process parameters to calibrate key parameters in the model (such as carrier mobility, oxide layer capacitance, etc.) to ensure model accuracy.

[0037] Extracting the transverse carrier density distribution: Based on the calibrated model, simulate or calculate the carrier density distribution in the transverse direction (perpendicular to the current direction) of the channel.

[0038] (2) Defect impact analysis: including hot carrier stress-induced interface states (N it ), Analysis of mobility degradation mechanism and quantification of N it Density. Among them, the thermal carrier stress-induced interface states (N it ): Applying hot carrier stress to the device to simulate the degradation process under actual operating conditions and induce interface states (N it ) generated. N it As a Coulomb scattering center, it reduces carrier mobility and affects device performance.

[0039] Analyze the mobility degradation mechanism: Investigate the types of scattering induced by Nit (such as ionized impurity scattering) and their quantitative impact on mobility. Combine experiments or simulations to analyze the physical mechanisms of mobility degradation (such as changes in scattering cross-section and carrier effective mass).

[0040] Quantization N it Density: The numerical distribution of the interface state density (Nit) is quantified by electrical tests (such as CV characteristic measurements) or charge pumping techniques.

[0041] (3) Defect spatial distribution extraction: This may include introducing the "channel slicing" theory (dividing the channel into multiple discrete slices, assuming that the parameters in each slice are uniform, which is convenient for local analysis), equivalent to a ballistic transistor chain (converting the traditional drift-diffusion transport model into a ballistic transport chain model, simplifying carrier transport analysis), analyzing carrier velocity and density degradation (calculating the carrier velocity saturation and density reduction caused by the hot carrier effect in each ballistic transistor slice), and constructing an interface state spatial distribution model (integrating Nit density quantization results and slice analysis data to establish a spatial distribution model of interface states in the channel).

[0042] This invention first uses a simplified EKV model to characterize the electrical behavior of small-sized devices. It establishes the relationship between gate-source voltage and normalized charge using the Lambert-W function, and ensures that key model parameters (such as threshold voltage, drain-induced barrier reduction effect factor, and ideality factor) accurately match the original IV characteristics of the device by calibrating them. This guarantees the physical basis of the model in its undegraded state. Furthermore, it calibrates with TCAD simulation data to extract the lateral carrier density, providing a basis for damage localization. Next, it considers the influence of hot carrier-induced interface states Nit on carrier mobility by monitoring the device's transconductance. A mobility-based calibration method, combined with IV characteristic matching before and after aging, is used to indirectly quantify the interface state density. Then, it introduces the "channel slicing" theory, equating drift-diffusion transistors to a series of ballistic transistor chains. The local degradation caused by hot carriers is represented as the degradation of carrier velocity and density in each corresponding ballistic transistor. Finally, a perturbation sensitivity model integrates the degradation effects of all "slices" to analyze the spatial distribution of interface states. Next, each step in Figure 1 will be described in detail: Step 110, basic modeling and calibration, uses a simplified EKV (sEKV, charge-based) model to characterize the electrical behavior of small-sized devices. Specific implementation steps may include: characterizing the electrical behavior of the target-size device using an sEKV model; the sEKV model uses the Lambert-W function to establish the relationship between the gate-source voltage and the normalized charge; the Lambert-W function is expressed as formula (1): (1); where, Represents normalized charge. The lambbert-w function, a product logarithmic function, is defined as f(w) = w·e w inverse function, V represents the gate-source voltage, VTH represents the threshold voltage, DIBL represents the drain-induced barrier reduction effect factor, and NIDE represents the ideality factor. Therefore, NIDE = SS / [ut × ln(10)], V D Indicates the drain voltage. The thermal voltage is expressed as kT / q; key model parameters are calibrated; the key model parameters include at least one of the threshold voltage VTH, drain-induced barrier reduction effect factor DIBL, and ideality factor NIDE; to ensure that they can accurately match the original IV characteristics of the device, thereby ensuring the physical basis of the model in the undegraded state.

[0043] After calibration with TCAD simulation data, the transverse carrier density is extracted, specifically using formula (2): (2); Extract the transverse carrier density from the carrier transport characteristic parameters to provide a basis for damage localization; among which, Represents the transverse carrier density. Represents the coefficient. Indicates the inversion coefficient. Indicates horizontal position. Indicates the effective length of the channel.

[0044] In step 120, the defect impact analysis considers the influence of hot carrier-induced interface states Nit on carrier mobility by monitoring the transconductance of the device: as VG increases, the transconductance gradually converges, and no further decrease in mobility is observed at higher VGs. This trend reflects the physical characteristics of the generated interface states, which act as additional Coulomb scattering centers, thus reducing mobility only in the Coulomb scattering confinement region (μco). Therefore, the focus is on analyzing the mobility reduction effect caused by them as Coulomb scattering centers, and calculating the actual mobility using the formula. Specifically, step 120 may include: analyzing the influence trend of hot carrier-induced interface states on carrier mobility by monitoring changes in the transconductance of the device; analyzing the carrier mobility reduction effect caused by the interface states as Coulomb scattering centers based on the influence trend; and using formula (3) based on the mobility reduction effect. (3); Calculate the actual migration rate; where, This represents the mobility of the Coulomb scattering-confined region when considering interface states. This represents the mobility of the Coulomb scattering-confined region when the interface states are zero. Represents the density of interface states. This represents the reference interface state density; a calibration method based on the mobility model, combined with IV characteristic matching before and after aging, achieves indirect quantification of the interface state density.

[0045] In step 130, defect spatial distribution extraction is achieved by introducing the "channel slicing" theory, which equates the drift-diffusion transistor to a series of ballistic transistor chains. First, the concept of "channel slicing" is explained with reference to Figure 3: As shown in Figure 3, "Drift-Diffusion MOSFET" represents a drift-diffusion metal-oxide-semiconductor field-effect transistor, a MOSFET model. In this model, the movement of charge carriers (electrons or holes) in the channel is mainly described by drift motion (affected by the electric field) and diffusion motion (affected by the carrier concentration gradient). "Virtual Reservoirs" represent virtual reservoirs (virtual source / drain regions, which can be understood as virtual carrier storage regions). When the channel is divided into multiple parts, these virtual storage regions are used to simulate the input and output relationships of charge carriers between different channel slices. "Ballistic MOSFET" stands for Ballistic Metal-Oxide-Semiconductor Field-Effect Transistor. When the size of a MOSFET is shrunk to the nanometer scale, the mean free path of charge carriers in the channel may be greater than the channel length. In this case, charge carriers transport between the source and drain regions with almost no scattering; this transport method is called ballistic transport, and a MOSFET with this characteristic is a ballistic MOSFET. VG is the gate voltage, VS is the source voltage, and VD is the drain voltage. In Figure 3, in the drift-diffusion MOSFET model on the left, current transport mainly occurs through the drift and diffusion processes of charge carriers. The movement of charge carriers is influenced by the electric field and concentration gradient. The ballistic MOSFET model on the right introduces the concept of virtual resistance. In this model, the channel is divided into multiple segments, each connected by a virtual resistor. This is the channel slicing process, where the entire channel is viewed as composed of multiple discrete slices. Carrier transport within each slice can be approximated as ballistic transport (i.e., carriers do not undergo scattering during transport). By dividing the channel into multiple slices, the analysis of carrier transport in the channel can be simplified. For nanodevices where ballistic transport is dominant, the traditional drift-diffusion model is no longer applicable. The channel slicing method combined with virtual resistance can more accurately describe the carrier transport behavior in the channel, thereby improving the accuracy of the model and better considering quantum effects and ballistic transport phenomena.

[0046] The defect spatial distribution extraction of this invention is achieved by introducing the "channel slicing" theory, which equates drift-diffusion transistors to a series of ballistic transistor chains. The local degradation caused by hot carriers can be expressed as the degradation of carrier velocity and density in each corresponding ballistic transistor: the former is achieved by modifying the original carrier velocity distribution v d This is achieved by converting it into an equivalent local mobility field product μF (Equation (4)), and then due to N it For μ coThe degradation is caused by the influence of position, and the carrier density degradation is captured by the corresponding Nit-induced local VTH and NIDE shifts, as shown in Equation (5-7), where position-dependent Mapped from the original carrier density distribution of each ballistic transistor. Specifically, step 130 may include: equating the drift-diffusion transistor to a chain of ballistic transistors in series; representing the local degradation caused by the hot carriers as the degradation of carrier velocity and carrier density in each ballistic transport unit; and constructing an interface state spatial distribution model by integrating the degradation effects of all “slices” (i.e., integrating the degradation of carrier velocity and carrier density in all ballistic transport units) through a perturbation sensitivity model, and analyzing the spatial distribution of the interface states.

[0047] The degradation of carrier velocity is converted into an equivalent local mobility field product, expressed as Equation (4): (4); among which, This represents the carrier velocity of the Nth ballistic transport unit. Represents the local mobility field product. Indicates the carrier saturation velocity. This represents a coefficient that reflects the velocity saturation effect caused by the electric field.

[0048] The degradation of carrier density is captured by the local threshold voltage shift and local ideality factor shift caused by interface states, as shown in equations (5)-(7): (5); (6); (7); among which, This represents the threshold voltage considering interface state deterioration. This represents the ideal factor that considers the deterioration of the interface state. Indicates oxide layer capacitance. This represents the carrier concentration of the Nth ballistic transport unit. This represents the gate voltage associated with the mapping position based on the original carrier density distribution of each ballistic transistor.

[0049] The disturbance sensitivity model is expressed as: (8); among which, Indicates drain current. Indicates the gate width. The total number of ballistic transmission units. This represents the carrier surface density of the Nth ballistic transport unit. This represents the carrier drift velocity of the Nth ballistic transport unit.

[0050] This invention establishes a local transport characteristic model under the influence of Coulomb scattering, and achieves accurate quantitative analysis of carrier transport degradation caused by interface states by quantitatively correcting the carrier mobility and local threshold voltage drift under the influence of Coulomb scattering. Secondly, the transistor channel is equivalently discretized into multiple ballistic transport units ("channel slices") in the spatial dimension, and combined with the spatial distribution analytical model of carrier surface density and drift velocity, the non-uniform spatial distribution characteristics of interface states in the channel are quantitatively characterized.

[0051] Based on the same idea, the present invention also provides a device for extracting the interface state density and distribution, as shown in Figure 4. The device may include: a model building and calibration module 410, configured to establish a physical model characterizing the intrinsic electrical behavior of the device, calibrate the physical model to obtain a reference model, and determine the carrier transport characteristic parameters; an interface state density determination module 420, configured to analyze the carrier mobility change caused by the interface state as a Coulomb scattering center based on the reference model, and determine the interface state density; and a defect spatial distribution extraction module 430, configured to equivalently discretize the transistor channel into multiple ballistic transport units in the spatial dimension, and quantitatively characterize the non-uniform spatial distribution characteristics of the interface state in the channel according to the carrier transport characteristic parameters and the interface state density.

[0052] Based on the device in Figure 4, further specific implementation units may be included: Optionally, the model building and calibration module 410 may include: an electrical behavior characterization unit, configured to characterize the electrical behavior of the target-size device using an sEKV model; the sEKV model uses the Lambert-W function to establish the relationship between the gate-source voltage and the normalized charge; the Lambert-W function is expressed as: ;in, Represents normalized charge. The lambbert-w function, a product logarithmic function, is defined as f(w) = w·e w inverse function, V represents the gate-source voltage, VTH represents the threshold voltage, DIBL represents the drain-induced barrier reduction factor, and NIDE represents the ideality factor. D Indicates the drain voltage. Represents thermal voltage; a key model parameter calibration unit is configured to calibrate key model parameters; the key model parameters include at least one of threshold voltage, drain-induced barrier reduction effect factor, and ideality factor; using the formula: The transverse carrier density extraction unit is configured to extract the transverse carrier density from the carrier transport characteristic parameters; wherein, Represents the transverse carrier density. Represents the coefficient. Indicates the inversion coefficient. Indicates horizontal position. Indicates the effective length of the channel.

[0053] Optionally, the interface state density determination module 420 may include: a carrier mobility influence trend determination unit, configured to analyze the influence trend of hot carrier-induced interface states on carrier mobility by monitoring changes in device transconductance; a carrier mobility reduction effect determination unit, configured to analyze the carrier mobility reduction effect caused by interface states as Coulomb scattering centers based on the influence trend; and an actual mobility calculation unit, configured to calculate the actual mobility based on the mobility reduction effect using the formula: ; Calculate the actual migration rate; where, This represents the mobility of the Coulomb scattering-confined region when considering interface states. This represents the mobility of the Coulomb scattering-confined region when the interface states are zero. Represents the density of interface states. The reference interface state density is represented by the interface state density indirect quantization unit, which is configured to indirectly quantize the interface state density based on the actual mobility.

[0054] Optionally, the defect spatial distribution extraction module 430 may include: a channel slicing unit configured to equate drift-diffusion transistors to a series of ballistic transistor chains; a local degradation equivalent unit configured to represent the local degradation caused by hot carriers as the degradation of carrier velocity and carrier density in each ballistic transport unit; and an interface state spatial distribution analysis unit configured to integrate the degradation of carrier velocity and carrier density in all ballistic transport units through a perturbation sensitivity model to construct an interface state spatial distribution model and analyze the spatial distribution of interface states.

[0055] Optionally, the degradation of the carrier velocity is converted into an equivalent local mobility field product representation: ;in, This represents the carrier velocity of the Nth ballistic transport unit. Represents the local mobility field product. Indicates the carrier saturation velocity. This represents a coefficient that reflects the velocity saturation effect caused by the electric field.

[0056] Optionally, the degradation of the carrier density is captured by local threshold voltage shift and local ideality factor shift caused by interface states: ; ; ;in, This represents the threshold voltage considering interface state deterioration. This represents the ideal factor that considers the deterioration of the interface state. Indicates oxide layer capacitance. This represents the carrier concentration of the Nth ballistic transport unit. This represents the gate voltage associated with the mapping position based on the original carrier density distribution of each ballistic transistor.

[0057] Optionally, the disturbance sensitivity model is expressed as: ;in, Indicates drain current. Indicates the gate width. The total number of ballistic transmission units. This represents the carrier surface density of the Nth ballistic transport unit. This represents the carrier drift velocity of the Nth ballistic transport unit.

[0058] Based on the same approach, this specification also provides a device for extracting device interface state density and distribution. As shown in Figure 5, the device includes: a memory, a processor, and a communication interface coupled to the processor; the memory stores a computer program that can be run by the processor; when the processor runs the computer program, it executes the aforementioned device interface state density and distribution extraction method.

[0059] As shown in Figure 5, the processor described above can be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of the program of the present invention. The communication interface described above can be one or more. The communication interface can use any transceiver-like device for communicating with other devices or communication networks. As shown in Figure 5, the terminal device described above may also include a communication line. The communication line may include a path for transmitting information between the components described above.

[0060] Optionally, as shown in Figure 5, the terminal device may further include a memory. The memory stores a computer program executable by the processor; when the processor runs the computer program, it implements the method provided in this embodiment of the invention. As shown in Figure 5, the memory may be a read-only memory (ROM) or other types of static storage devices capable of storing static information and instructions, random access memory (RAM) or other types of dynamic storage devices capable of storing information and instructions, or it may be an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), a magnetic disk storage medium or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but is not limited thereto. The memory may exist independently and be connected to the processor via a communication line. The memory may also be integrated with the processor.

[0061] Optionally, the computer execution instructions in the embodiments of the present invention may also be referred to as application code, and the embodiments of the present invention do not specifically limit this.

[0062] In a specific implementation, as shown in Figure 5, the processor may include one or more CPUs, such as CPU0 and CPU1 in Figure 5.

[0063] In a specific implementation, as shown in Figure 5, the terminal device may include multiple processors. Each of these processors may be a single-core processor or a multi-core processor.

[0064] Based on the same idea, this specification also provides a computer storage medium corresponding to the above embodiments. The computer storage medium stores instructions that, when executed, implement the methods in the above embodiments.

[0065] The foregoing mainly describes the solutions provided by the embodiments of the present invention from the perspective of the interaction between various modules. It is understood that each module, in order to achieve the above functions, includes corresponding hardware structures and / or software units for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments disclosed herein, the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed by hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0066] The embodiments of the present invention can divide functional modules according to the above method examples. For example, each function can be divided into its own functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware or as a software functional module. It should be noted that the module division in the embodiments of the present invention is illustrative and only represents one logical functional division; other division methods may be used in actual implementation.

[0067] The processor described in this specification may also function as a memory. The memory stores computer execution instructions for carrying out the present invention, and its execution is controlled by the processor. The processor executes the computer execution instructions stored in the memory, thereby implementing the method provided in the embodiments of the present invention.

[0068] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0069] It is obvious that various modifications and combinations can be made without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for extracting the density and distribution of states at a device interface, characterized in that, The method includes: establishing a physical model characterizing the intrinsic electrical behavior of the device; calibrating the physical model to obtain a reference model; and determining the carrier transport characteristic parameters; based on the reference model, analyzing the carrier mobility change caused by the interface states as Coulomb scattering centers, and determining the interface state density; and equivalently discretizing the transistor channel into multiple ballistic transport units in the spatial dimension, and quantitatively characterizing the non-uniform spatial distribution characteristics of the interface states in the channel according to the carrier transport characteristic parameters and the interface state density.

2. The method according to claim 1, characterized in that, A physical model characterizing the intrinsic electrical behavior of the device is established, and the physical model is calibrated to obtain a baseline model. Carrier transport characteristic parameters are determined, including: characterizing the electrical behavior of the target-size device using the sEKV model; the sEKV model uses the Lambert-W function to establish the relationship between the gate-source voltage and the normalized charge; the Lambert-W function is expressed as: ;in, Represents normalized charge. Let the lambbertw function be the product logarithm function, defined as follows: inverse function, V represents the gate-source voltage, VTH represents the threshold voltage, DIBL represents the drain-induced barrier reduction factor, and NIDE represents the ideality factor. D Indicates the drain voltage. Representing thermal voltage; calibrating key model parameters; the key model parameters include at least one of threshold voltage, leakage-induced barrier reduction effect factor, and ideality factor; using the formula: Extract the transverse carrier density from the carrier transport characteristic parameters; where, Represents the transverse carrier density. Represents the coefficient. Indicates the inversion coefficient. Indicates horizontal position. Indicates the effective length of the channel.

3. The method according to claim 2, characterized in that, Based on the aforementioned benchmark model, the carrier mobility variation caused by interface states as Coulomb scattering centers is analyzed, and the interface state density is determined. This includes: analyzing the influence trend of hot carrier-induced interface states on carrier mobility by monitoring changes in device transconductance; analyzing the carrier mobility reduction effect caused by interface states as Coulomb scattering centers based on the influence trend; and using the formula based on the mobility reduction effect: ; Calculate the actual migration rate; where, This represents the mobility of the Coulomb scattering-confined region when considering interface states. This represents the mobility of the Coulomb scattering-confined region when the interface states are zero. Represents the density of interface states. The reference interface state density is represented; the interface state density is indirectly quantized based on the actual mobility.

4. The method according to claim 3, characterized in that, The transistor channel is spatially discretized into multiple ballistic transport units. Based on the carrier transport characteristics and interface state density, the non-uniform spatial distribution characteristics of the interface states within the channel are quantitatively characterized. This includes: equating the drift-diffusion transistor to a series of ballistic transistor chains; representing the local degradation caused by hot carriers as the degradation of carrier velocity and carrier density in each ballistic transport unit; and integrating the degradation of carrier velocity and carrier density in all ballistic transport units through a perturbation sensitivity model to construct an interface state spatial distribution model and analyze the spatial distribution of the interface states.

5. The method according to claim 4, characterized in that, The degradation of the carrier velocity is converted into an equivalent local mobility field product representation: ;in, This represents the carrier velocity of the Nth ballistic transport unit. Represents the local mobility field product. Indicates the carrier saturation velocity. This represents a coefficient that reflects the velocity saturation effect caused by the electric field.

6. The method according to claim 4, characterized in that, The degradation of the carrier density is captured by the local threshold voltage shift and the local ideality factor shift caused by the interface states: ； ； ;in, This represents the threshold voltage considering interface state deterioration. This represents the ideal factor that considers the deterioration of the interface state. Indicates oxide layer capacitance. This represents the carrier concentration of the Nth ballistic transport unit. This represents the gate voltage associated with the mapping position based on the original carrier density distribution of each ballistic transistor.

7. The method according to claim 4, characterized in that, The disturbance sensitivity model is expressed as follows: ;in, Indicates drain current. Indicates the gate width. The total number of ballistic transmission units. This represents the carrier surface density of the Nth ballistic transport unit. This represents the carrier drift velocity of the Nth ballistic transport unit.

8. A device for extracting the density and distribution of interface states of a device, characterized in that, The apparatus is applied to the device interface state density and distribution extraction method according to any one of claims 1 to 7, the apparatus comprising: a model building and calibration module configured to establish a physical model characterizing the intrinsic electrical behavior of the device, calibrate the physical model to obtain a reference model, and determine carrier transport characteristic parameters; an interface state density determination module configured to analyze the carrier mobility change caused by the interface state as a Coulomb scattering center based on the reference model, and determine the interface state density; and a defect spatial distribution extraction module configured to equivalently discretize the transistor channel into multiple ballistic transport units in the spatial dimension, and quantitatively characterize the non-uniform spatial distribution characteristics of the interface state in the channel according to the carrier transport characteristic parameters and the interface state density.

9. A device for extracting the density and distribution of interface states of a device, characterized in that the device... include: Memory, processor, and communication interface coupled to the processor; The memory stores computer programs that can be executed by the processor; When the processor runs the computer program, it performs the device interface state density and distribution extraction method as described in any one of claims 1 to 7.

10. A computer storage medium, characterized in that, The computer storage medium stores instructions that, when executed by the processor, implement the device interface state density and distribution extraction method according to any one of claims 1 to 7.

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