A method of modeling a mos device

Abstract

The application relates to the technical field of semiconductors, and discloses a modeling method of a MOS device, which comprises discretizing the geometric structure of the MOS device into a three-dimensional cell grid, and defining a state vector containing multi-physical field information for each cell in the three-dimensional cell grid, wherein the state vector at least comprises: carrier density and local electric potential for representing electrical characteristics, carrier average energy for representing quantum effects, local temperature for representing thermal effects, and defect state for representing reliability effects; and for simulating process variability of the device, the initial defect state of each cell in the three-dimensional cell grid is randomly set when the state vector is defined. A double-layer adaptive evolution rule system composed of a meta-learning rule layer and a basic rule layer is set, and the meta-learning rule layer can dynamically adjust the basic rule parameter set used by the basic rule layer according to the local macro state in the neighborhood of each cell.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor, in particular to a modeling method of MOS device. BACKGROUND

[0002] Traditional device modeling methods, technical computer-aided design tools, usually solve a set of coupled, macroscopic partial differential equations, such as drift-diffusion equations, Poisson equations and heat conduction equations, to describe the electrical and thermal characteristics of the device. When the key size of the device enters the deep nanometer scale, various previously negligible physical effects become more and more significant, and have a decisive influence on the performance of the device.

[0003] The prior art solution usually adopts an external coupling or sequential solving manner between multiple independent physical models when dealing with these highly coupled multi-physical field problems. First, electrical simulation is performed, then the power loss generated is taken as the input of thermal simulation, and the calculated temperature distribution is fed back to the electrical model to correct the parameters. This loose coupling method may not accurately capture the instantaneous and close interaction between different physical fields, the rapid change of local temperature on the instantaneous influence of carrier mobility, and the instantaneous feedback of the generated Joule heat.

[0004] The traditional continuum model equivalent of doped atoms and defects is a smooth continuous distribution, which is difficult to describe the random fluctuation phenomenon originating from the microscopic discreteness from the physical level. Although statistical methods can be introduced to model variability, these methods are usually external processing based on deterministic models, rather than fundamentally unified description.

[0005] Existing reliability models are usually based on empirical formulas or simplified macroscopic physical models, which have limitations in describing the degradation phenomenon with complex time dependence, and are difficult to accurately depict the non-Markov process with "memory effect".

[0006] Therefore, there is an urgent need in the art for a new device modeling technical solution that can intrinsically and self-consistently couple multiple physical effects such as electricity, heat, quantum, variability and reliability in a unified physical framework, to meet the demand for high-precision predictive simulation of MOS devices at advanced process nodes. SUMMARY

[0007] In view of the deficiencies of the prior art, the present application provides a modeling method of MOS device, which solves the problem that the prior art is difficult to self-consistently describe the coupling effects of multiple physical fields and intrinsic process variability in a unified framework when modeling advanced MOS devices.

[0008] To achieve the above object, the present application is implemented by the following technical solutions: a modeling method of a MOS device, comprising:

[0009] First, the geometric structure of the MOS device is discretized into a three-dimensional cell grid, and a state vector containing multi-physical field information is defined for each cell in the three-dimensional cell grid.

[0010] The state vector at least includes: carrier density and local electric potential for characterizing electrical characteristics, carrier average energy for characterizing quantum effects, local temperature for characterizing thermal effects, and defect state for characterizing reliability effects. To simulate the process variability of the device, the initial defect state of each cell in the three-dimensional cell grid is randomly set when the state vector is defined.

[0011] After the cell and its state vector are defined, the dynamic behavior of the device is simulated by iteratively updating the state vector of each cell within a discrete time step. This iterative update is realized by a double-layer adaptive evolution rule system.

[0012] The double-layer adaptive evolution rule system includes a meta-learning rule layer and a basic rule layer.

[0013] The function of the meta-learning rule layer is to dynamically adjust a set of basic rule parameters in the basic rule layer corresponding to each cell according to the local macro state in the neighborhood of the cell. The adjustment process includes: first, calculating the average value of the state vector components in the neighborhood of the cell to obtain the local macro state; then, updating the set of basic rule parameters according to the obtained local macro state through a preset mapping function. The set of basic rule parameters at least includes: at least one of carrier mobility, scattering rate, thermal conductivity, and defect capture cross section.

[0014] The update of the set of basic rule parameters can be realized by the following formula:

[0015] ;

[0016] wherein, is the cell index, is the current time step, is the time step, is the preset mapping function, is the local macro state of the cell at time , is a set of fixed global meta parameters.

[0017] The function of the base rule layer is to calculate the evolution of the state vector over discrete time using the base rule parameter set adjusted by the meta-learning rule layer. This evolution calculation includes several aspects:

[0018] First, the carrier transport between cells is calculated. This calculation is based on the difference in local potential and the difference in carrier average energy between adjacent cells, and uses the transport-related coefficients in the base rule parameter set to calculate the carrier transition probability between cells. The calculation of the carrier transition probability from a cell to an adjacent cell includes the following dependencies:

[0019] ;

[0020] where, is the transition function, is the difference in local potential between cell and , is the difference in carrier average energy between cell and , is the base rule parameter set in S2 adjusted by the meta-learning rule layer.

[0021] Second, the local potential is updated. This update is based on the discrete form of the Poisson equation, which updates the local potential of each cell according to the net charge density determined by the carrier density and the defect state in the cell and its neighborhood.

[0022] Third, the local temperature is updated. This update is based on the temperature gradient between cells and takes into account the Joule heat source term generated by carrier transport.

[0023] The state vector also includes a historical path state, which is used to record the evolution trajectory of the defect state over a plurality of discrete time steps in the past, to realize the modeling of non-Markovian effects in device reliability.

[0024] After the iterative update, the macroscopic electrical characteristics of the MOS device are extracted according to the obtained cell state vector. The end-point current of the MOS device is calculated by integrating the net carrier flux through the boundary cells representing the electrodes of the device.

[0025] The present application provides a modeling method for a MOS device. It has the following advantages:

[0026] ​1、The present application sets up the double-layer self-adaptive evolution rule system composed of the meta-learning rule layer and the basic rule layer, the meta-learning rule layer can dynamically adjust the basic rule parameter set used by the basic rule layer according to the local macro state in each cell neighborhood, so that the physical parameters used by the model can automatically adapt to the non-uniform and dynamically changing physical environment inside the device, thereby improving the physical description accuracy of the model under different working bias and working conditions.

[0027] 2、The present application integrates multiple physical quantities for characterizing electrical, quantum, thermal and reliability effects into a single cell state vector, and iteratively evolves under the same set of basic rule layer to realize intrinsic coupling modeling of multi-physical field effects; avoids the complexity and potential convergence problem of external coupling between multiple independent physical models, and can directly describe the influence of self-heating effect on carrier transport, the change of local electric potential caused by defect trapped charge and other closely coupled physical processes.

[0028] 3、The present application can generate a large number of different device instances conforming to specific process statistical characteristics at the microscopic level by randomizing the initial defect state of each cell when defining the initial state vector; by performing complete dynamic evolution simulation on these instances, the relationship between microscopic random fluctuations and macroscopic electrical characteristic statistical distribution can be directly established from the physical level, providing a technical approach for process variability analysis of devices. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The method flowchart of the present application. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0031] Embodiment:

[0032] Please refer to the accompanying Figure 1 The embodiment of the present application provides a modeling method of a MOS device, comprising the following steps:

[0033] S1, discretize the geometric structure of the MOS device into a three-dimensional cell grid, and define a state vector containing multi-physical field information for each cell in the three-dimensional cell grid,

[0034] The state vector at least includes: carrier density and local electric potential for characterizing electrical characteristics, carrier average energy for characterizing quantum effects, local temperature for characterizing thermal effects, and defect state for characterizing reliability effects; for simulating process variability of the device, the initial defect state of each cell in the three-dimensional cell grid is randomly set when the state vector is defined;

[0035] In the embodiment, step S1 performs spatial discretization processing on the MOS device, and establishes a complete physical state description for the discretized micro-units, to provide initial conditions and data structure basis for subsequent dynamic evolution simulation.

[0036] The set geometry refers to the complete internal and external three-dimensional space structure of the MOS device, including the spatial layout, size of all components and the interface therebetween.

[0037] First, according to the given three-dimensional geometry of the MOS device to be modeled, the continuous physical space is discretized into a three-dimensional cell grid . The grid is composed of a large number of closely adjacent cells , wherein is the unique index of the cell. Each cell is given a material attribute to distinguish it as a semiconductor, insulator or conductor, etc. The size of the cell can be set according to the requirement of simulation accuracy, to balance between computing resources and physical detail description.

[0038] After completing the geometric discretization, a state vector of each cell in the three-dimensional cell grid is defined at a discrete time point . The state vector aims to intrinsically contain the core information required by the internal multi-physical field coupling effect of the device through a unified data structure. The definition of the state vector is the basis for all subsequent evolution calculations of the present application. Its specific composition can be represented by the following formula:

[0039] ;

[0040] In this definition, each component of the state vector has a clear physical meaning and serves a specific modeling goal:

[0041] The carrier density and the local electric potential are the core components for characterizing the basic electrical characteristics in the cell. represents the free carrier concentration in the cell, and describes the potential level at the point.

[0042] To realize the description of quantum effects, the state vector contains the carrier average energy In MOS devices at nanometer scale, the energy states of carriers can deviate from equilibrium due to quantum confinement effect and high field transport. Introducing the average energy of carriers as an independent state variable enables the subsequent evolution rules to take the energy states of carriers as input, thus indirectly accounting for the effects of hot carrier effect, partial quantum tunneling effect, etc. on device performance.

[0043] To realize the description of thermal effect, the local temperature is included in the state vector . The component is used to characterize the lattice temperature of the cell . Due to high power density, self-heating effect is significant in devices under advanced process. The inclusion of local temperature in the state vector enables the subsequent evolution to account for the conduction process of the heat generated by Joule heat inside the device, thus realizing the bidirectional coupling modeling between electricity and heat.

[0044] To realize the description of reliability effect, the defect state is included in the state vector . The component is a set, which is used to record the physical properties of various point defects existing inside the cell

[0045] and their current charge occupation state. By simulating the capture and emission process of defects on carriers in the subsequent evolution, the bias temperature instability, hot carrier injection, etc. reliability degradation phenomenon can be modeled. To model the reliability degradation process with memory effect, the history path state is also included in the state vector

[0046] . The history path state is used to record the evolution trajectory of the defect state in the past multiple discrete time steps, to realize the modeling of non-Markov effect in device reliability. The component is a data structure, a first-in-first-out queue, which is used to store the evolution trajectory of the defect state in the past several discrete time steps. When calculating some defect-related evolution probabilities, not only the current system state, but also the recent history state can be referred to. After completing the structure definition of the state vector, it needs to be initialized, that is, to set the initial state of the system at

[0047] S2, simulating the dynamic behavior of the device by iteratively updating the state vector of each cell in discrete time steps, wherein the iteratively updating is implemented by a double-layer adaptive evolution rule system comprising a meta-learning rule layer and a base rule layer:

[0048] With the meta-learning rule layer, a set of base rule parameters in the base rule layer corresponding to each cell is dynamically adjusted according to a local macro state in the neighborhood of the cell; preferably, it specifically comprises:

[0049] The average value of the state vector components in the neighborhood of the each cell is calculated to obtain the local macro state;

[0050] Then, the set of base rule parameters is updated according to the local macro state by a preset mapping function.

[0051] With the base rule layer, the evolution of the state vector over discrete time is calculated using the set of base rule parameters adjusted by the meta-learning rule layer; preferably, it further comprises: updating the local potential: the updating is based on the discrete form of the Poisson equation, and the local potential of each cell is updated according to the net charge density determined by the carrier density and the defect state in the neighborhood of the cell.

[0052] The double-layer adaptive evolution rule system is a hierarchical computing structure, wherein the upper layer (the meta-learning rule layer) dynamically adjusts the calculation parameters according to the local state of the system, and the lower layer (the base rule layer) uses the set of adjusted parameters to specifically perform the evolution calculation of the system state; the meta-learning rule layer is a computing level, and its function is to dynamically adjust and output a set of physical parameters for the base rule layer to use for performing specific evolution calculation according to the local macro state inside the system; the base rule layer is a computing level, and its function is to use the set of base rule parameters dynamically adjusted by the meta-learning rule layer to specifically perform the evolution calculation of the state vector from the current time step to the next time step; the local macro state is a physical quantity obtained by spatial processing of the state vector components of each cell in the neighborhood of a cell, which is used to represent the local physical environment of the cell, such as local average carrier energy, local electric field gradient or local temperature, etc.

[0053] In this embodiment, step S2 is the core execution link for implementing the dynamic behavior simulation of the MOS device. In this step, the state vectors of all cells defined in step S1 are iteratively updated by the double-layer adaptive evolution rule system in discrete time steps to obtain the state at the next time. .

[0054] The double-layer adaptive evolution rule system includes a meta-learning rule layer and a basic rule layer, both of which work in sequence at each time step.

[0055] First, the operation of the meta-learning rule layer is performed. The function of this layer is not to directly calculate the evolution of the state vector, but to provide a set of adaptive basic rule parameters that match the current local physical environment for the basic rule layer that will perform the evolution calculation.

[0056] Specifically, for a cell , the meta-learning rule layer first calculates the local macrostate within its neighborhood . This local macrostate is a scalar or vector obtained by spatially averaging the state vector components of the cells in the neighborhood, representing the local physical environment in which the cell is located.

[0057] Then, the meta-learning rule layer dynamically adjusts and outputs a set of basic rule parameters that the cell will use at the next time step according to the just obtained local macrostate through a preset mapping function . This updating process can be described by the following formula:

[0058]

[0059] where is the cell index, is the current time step, is the time step length. is the preset mapping function, determined before modeling begins, which can be an analytical function or a lookup table. is the local macrostate of cell at time as input. is a set of fixed, global meta-parameters used to calibrate the specific form of the mapping function .

[0060] The basic rule parameter set includes a plurality of key physical parameters. This set includes at least one of the carrier mobility for determining the carrier drift-diffusion behavior, the scattering rate for describing the high-energy carrier energy relaxation process, the material thermal conductivity for describing the lattice heat conduction ability, and the defect capture cross-section for describing the defect capture and emission dynamics.

[0061] After the meta-learning rule layer completes the dynamic adjustment of the basic rule parameter set for all cells, the basic rule layer uses this fresh, localized parameter set to specifically calculate the state vector of each cell​ to the evolution of the state vector. This computation is performed in parallel on all cells and updates each component of the state vector according to physical conservation laws.

[0062] For the evolution of the electrical and quantum-related components of the state vector, the core of the computation lies in determining the carrier transition probability between a cell and its neighboring cells . This probability is computed based on the local potential difference and the carrier average energy difference between neighboring cells, and directly calls the transport-related parameters contained in the base rule parameter set provided by the meta-learning rule layer. The dependency of this computation can be expressed as:

[0063]

[0064] where is the transition function that describes the physical mechanism of the specific transition, whose internal parameters are all provided by . By computing the transition probability between a cell and all its neighbors, the net carrier flux can be obtained, thus updating the carrier density and the carrier average energy according to the energy gain or loss during the transport process.

[0065] To ensure the self-consistency of the potential distribution, the computation of the state vector evolution at discrete time using the base rule layer also includes updating the local potential . According to the net charge density within each cell and its neighborhood, which is jointly determined by the current carrier density and the defect state , a new potential distribution that matches this charge distribution is solved.

[0066] For the evolution of the thermal component , the computation of the state vector evolution at discrete time using the base rule layer also includes updating the local temperature. This update is based on the temperature gradient between cells to compute the heat flux, while the Joule heat generated during the carrier transport process is taken into account as a source term. The thermal conductivity required for the computation of the heat flux is also dynamically adjusted by the meta-learning rule layer according to the local state.

[0067] Through the above series of calculations, a complete iteration of all cell state vectors from to is completed. This process will be repeated throughout the simulation time. ​​

[0068] S3, after the iteration update, according to the obtained cell state vector, extract the macroscopic electrical characteristics of the MOS device.

[0069] In this embodiment, step S3 is to process and analyze the obtained set of full-device cell state vectors containing rich microscopic physical information after the completion of the iterative evolution process in step S2, in order to extract key parameters that can represent the macroscopic electrical characteristics of the MOS device. This step is a bridge connecting microscopic physical simulation and macroscopic device performance characterization.

[0070] Specifically, this step is executed after the iteration update reaches a steady-state condition or reaches a preset simulation time length.

[0071] To extract the macroscopic electrical characteristics of the MOS device, the core task is to calculate its end-point current, drain current, source current and gate current. This calculation is achieved by integrating the net carrier flux across the boundary cells representing the electrodes of the device.

[0072] First, it is necessary to identify the set of cells that constitute each electrode of the device from the three-dimensional cell grid. These cells are usually boundary cells with conductor material properties connected to external voltage sources.

[0073] Then, taking the calculation of the drain current as an example, it is necessary to examine the carrier exchange between all cells located inside the drain electrode and their adjacent cells that do not belong to the drain electrode. In each iteration step of step S2, the carrier transition probability and net flux between all adjacent cells have actually been calculated. Therefore, when extracting macroscopic characteristics, only the summation of these microscopic fluxes is required. The calculation of the drain current can be described by the following formula:

[0074]

[0075] where, is the set of cells representing the drain electrode. The summation traverses all drain cells . The second summation traverses all neighbors of cell , those cells that do not belong to the drain electrode. is the net carrier flux from cell to cell at time . is the elementary charge. The microscopic carrier flow across the entire drain channel interface is integrated into the macroscopic end-point current.

[0076] It should be understood that a single execution of the complete procedure of steps S1 to S3 only gives the device response under a single combination of external bias voltages. To obtain the complete characteristic curve of the device, it is necessary to repeat the complete procedure of steps S2 to S3 under different combinations of external bias voltages, i.e. to perform a voltage sweep. To obtain the characteristic curve, the drain voltage can be fixed and then the gate voltage is swept with a certain step size, and the complete dynamic evolution and characteristic extraction procedure is performed for each gate voltage point, and finally the data of all scanned points are connected into a line. The rate of change of the gate capacitance characteristic of the device can be extracted by calculating the total amount of charge in the set of gate electrode cells

[0077] In addition, the state vector defined in the present application also supports the extraction of other macroscopic electrical characteristics. The total amount of charge in the set of gate electrode cells The rate of change of the gate capacitance characteristic of the device can be extracted by calculating the total amount of charge in the set of gate electrode cells

[0078] The reliability and variability of the device can be macroscopically characterized. The degree of degradation of the device can be quantified by simulating the change in the macroscopic characteristics of the device before and after it has experienced a long period of electrical or thermal stress, the threshold voltage drift For variability, since a large number of device instances with different microscopic defect distributions are generated in step S1, the complete procedure of steps S1 to S3 can be performed on the instances, thereby obtaining the statistical distribution of the macroscopic parameters. This statistical distribution directly reflects the fluctuation in the macroscopic device performance caused by microscopic randomness.

[0079] Although embodiments of the present application have been shown and described, it is to be understood that various modifications, substitutions, replacements and changes can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.​

Claims

1. A method of modeling a MOS device, characterized by, Comprising: S1, discretizing the geometry of the MOS device into a three-dimensional cell grid, and defining a state vector containing multi-physical field information for each cell in the three-dimensional cell grid, wherein the state vector at least includes: carrier density and local potential for characterizing electrical characteristics, carrier average energy for characterizing quantum effects, local temperature for characterizing thermal effects, and defect state for characterizing reliability effects; and, for simulating process variability of the device, the initial defect state of each cell in the three-dimensional cell grid is randomly set when defining the state vector; S2, simulating the dynamic behavior of the device by iteratively updating the state vector of each cell within a discrete time step, wherein the iterative update is realized by a double-layer adaptive evolution rule system, including a meta-learning rule layer and a basic rule layer: using the meta-learning rule layer, dynamically adjusting a set of basic rule parameter sets in the basic rule layer corresponding to each cell according to the local macroscopic state within the neighborhood of the cell; using the basic rule layer, calculating the evolution of the state vector over discrete time using the basic rule parameter set adjusted by the meta-learning rule layer; S3, after the iterative update, extracting the macroscopic electrical characteristics of the MOS device according to the obtained cell state vector.

2. The method of claim 1, wherein, In S2, using the meta-learning rule layer, dynamically adjusting a set of basic rule parameter sets in the basic rule layer corresponding to each cell according to the local macroscopic state within the neighborhood of the cell, specifically including: calculating the average value of the state vector components within the neighborhood of the cell to obtain the local macroscopic state; then updating the basic rule parameter set according to the local macroscopic state through a pre-set mapping function.

3. The method of claim 2, wherein, The basic rule parameter set at least includes: at least one of carrier mobility, scattering rate, thermal conductivity, and defect capture cross section.

4. The method of claim 2, wherein, The base rule parameter set is updated by the following equation: ； wherein, is the cell index, is the current time step, is the time step size, is the pre-defined mapping function, is the cell at time the local macro state, is a set of fixed global meta-parameters.

5. The method of claim 1, wherein, In S2, using the basic rule layer, calculating the evolution of the state vector over discrete time using the basic rule parameter set adjusted by the meta-learning rule layer, including calculating the carrier transport between cells: based on the difference between the local potential and the carrier average energy between adjacent cells, and using the transport-related parameters in the basic rule parameter set, to calculate the carrier transition probability between cells.

6. The method of claim 5, wherein, From a cell to an adjacent cell the probability of carrier transition computation, including the following dependencies: ； wherein, is a transition function, is a cell and a local potential difference between is a cell and a carrier average energy difference between is the base rule parameter set in S2 adjusted by the meta-learning rule layer.

7. The method of claim 1, wherein, In S2, using the basic rule layer, calculating the evolution of the state vector over discrete time using the basic rule parameter set adjusted by the meta-learning rule layer, also includes updating the local potential: the update is based on the discrete form of Poisson equation, and updates the local potential of each cell according to the net charge density determined by the carrier density and the defect state within the cell and its neighborhood.

8. The method of claim 1, wherein, In S2, using the basic rule layer, calculating the evolution of the state vector over discrete time using the basic rule parameter set adjusted by the meta-learning rule layer, also includes updating the local temperature: the update is based on the temperature gradient between cells and takes into account the Joule heat source term generated by carrier transport.

9. The method of claim 1, wherein, The state vector in S1 further comprises a history path state for recording the evolution trajectory of the defect state in past multiple discrete time steps to realize modeling of non-Markov effect in device reliability.

10. The method of claim 1, wherein, The extracting the macroscopic electrical characteristics of the MOS device in S3 specifically comprises: calculating the end-point current of the MOS device by integrating the net carrier flux passing through the boundary cell representing the electrode of the device.

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