Modeling method of MOS device

Abstract

The invention relates to the technical field of semiconductors, and discloses a modeling method of an MOS (Metal Oxide Semiconductor) device, which comprises the following steps: discretizing a geometric structure of the MOS device into a three-dimensional cellular grid, and defining a state vector containing multi-physical field information for each cell in the three-dimensional cellular grid, the state vectors at least comprise carrier density and local potential for representing electrical characteristics, carrier average energy for representing a quantum effect, local temperature for representing a heat effect, and a defect state for representing a reliability effect; moreover, for simulating the process variability of the device, when the state vector is defined, the initial defect state of each cell in the three-dimensional cell grid is subjected to randomization setting. By setting a double-layer adaptive evolution rule system formed by a meta-learning rule layer and a basic rule layer, the meta-learning rule layer can dynamically adjust a basic rule parameter set used by the basic rule layer according to a local macroscopic state in each cellular neighborhood.

Description

Technical Field

[0001] This invention relates to the field of semiconductor technology, specifically to a modeling method for MOS devices. Background Technology

[0002] Traditional device modeling methods, using computer-aided design tools, typically rely on solving a set of coupled, macroscopic partial differential equations, such as the drift-diffusion equation, the Poisson equation, and the heat conduction equation, to describe the electrical and thermal properties of devices. However, as the critical dimensions of devices approach the deep nanoscale, many previously negligible physical effects become increasingly significant and have a decisive impact on device performance.

[0003] Existing solutions for these highly coupled multiphysics problems typically employ external coupling or sequential solution methods between multiple independent physical models. First, an electrical simulation is performed, then the resulting power loss is used as input for a thermal simulation, and the calculated temperature distribution is fed back to the electrical model to correct parameters. This loosely coupled approach may fail to accurately capture the instantaneous and close interactions between different physical fields, the immediate impact of rapid changes in local temperature on carrier mobility, and this impact, in turn, on the immediate feedback of Joule heating.

[0004] Traditional continuum models equate doped atoms and defects to a smooth, continuous distribution, making it difficult to intrinsically describe the random fluctuations arising from microscopic discreteness at the physical level. While statistical methods can be introduced to model variability, these methods are often additional processing on top of deterministic models rather than providing a fundamental, unified description.

[0005] Existing reliability models are usually based on empirical formulas or simplified macroscopic physical models. These models have limitations in describing degradation phenomena with complex time-dependent characteristics and are difficult to accurately characterize non-Markovian processes with "memory effects".

[0006] Therefore, there is an urgent need in this field for a new device modeling technology that can intrinsically and self-consistently couple multiple physical effects such as electrical, thermal, quantum, variability and reliability within a unified physical framework, in order to meet the need for high-precision predictive simulation of MOS devices at advanced process nodes. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a modeling method for MOS devices, which solves the problem that existing technologies struggle to provide a self-consistent description of multi-physics coupling effects and intrinsic process variability within a unified framework when modeling advanced MOS devices.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a modeling method for a MOS device, comprising:

[0009] First, the geometry of the MOS device is discretized into a three-dimensional cellular mesh, and a state vector containing multiphysics information is defined for each cell in the three-dimensional cellular mesh.

[0010] The state vector includes at least: carrier density and local potential for characterizing electrical properties, average carrier energy for characterizing quantum effects, local temperature for characterizing thermal effects, and defect states for characterizing reliability effects. To simulate the process variability of the device, the initial defect states of each cell in the three-dimensional cellular grid are randomized when defining the state vector.

[0011] After defining the cells and their state vectors, the dynamic behavior of the device is simulated by iteratively updating the state vector of each cell within discrete time steps. This iterative update is implemented through a two-layer adaptive evolution rule system.

[0012] This two-layer self-adaptive evolutionary 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 based on the local macroscopic state in the neighborhood of each cell. This adjustment process includes: first, calculating the average value of the state vector components in the neighborhood of each cell to obtain the local macroscopic state; then, updating the basic rule parameter set according to the obtained local macroscopic state using a preset mapping function. The basic rule parameter set includes at least one of the following: carrier mobility, scattering rate, thermal conductivity, and defect trapping cross-section.

[0014] The basic rule parameter set The update can be achieved using the following formula:

[0015] ;

[0016] in, For cell indexing, For the current time step, For time step, For the preset mapping function, For cells In time The aforementioned local macroscopic state, It is a fixed set of global meta-parameters.

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

[0018] First, the inter-cell carrier transport is calculated. This calculation is based on the difference between the local potential and the average carrier energy between adjacent cells, and uses transport correlation coefficients from the set of fundamental rule parameters to calculate the inter-cell carrier transition probabilities. From the cell... to adjacent cells carrier transition probability The computation includes the following dependencies:

[0019] ;

[0020] in, For transition functions, For cells and The local potential difference between them For cells and The difference in average carrier energy between them This is the set of basic rule parameters in S2 after being adjusted by the meta-learning rule layer.

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

[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 historical path states, which are used to record the evolution trajectory of the defect state over multiple discrete time steps in the past, so as to model the non-Markovian effects in device reliability.

[0024] Following the iterative update, the macroscopic electrical characteristics of the MOS device are extracted based on the obtained cell state vector. The terminal current of the MOS device is calculated by integrating the net carrier flux through the boundary cells representing the device electrodes.

[0025] This invention provides a modeling method for MOS devices. It has the following advantages:

[0026] 1. This invention establishes a two-layer adaptive evolution rule system consisting of a meta-learning rule layer and a basic rule layer. The meta-learning rule layer can dynamically adjust the set of basic rule parameters used by the basic rule layer according to the local macroscopic state in the neighborhood of each cell, so that the physical parameters adopted by the model can automatically adapt to the non-uniform and dynamically changing physical environment inside the device, thereby improving the accuracy of the physical description of the model under different operating bias voltages and operating conditions.

[0027] 2. This invention integrates multiple physical quantities used to characterize electrical, quantum, thermal, and reliability effects into a single cell state vector and performs synchronous iterative evolution under the same set of basic rules, thereby realizing intrinsic coupling modeling of multi-physics field effects. It avoids the complexity and potential convergence problems of external coupling between multiple independent physical models and can directly describe tightly coupled physical processes such as the influence of self-heating effects on carrier transport and the change of local potential by defect-trapped charges.

[0028] 3. By randomly setting the initial defect state of each cell when defining the initial state vector, this invention can generate a large number of different device instances that conform to specific process statistical characteristics at the micro level. By performing complete dynamic evolution simulations on these instances, the connection between micro-random fluctuations and macro-electrical characteristic statistical distribution can be directly established from the physical level, providing a technical approach for the process variability analysis of devices. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

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

[0031] Example:

[0032] Please see the appendix Figure 1 This invention provides a modeling method for a MOS device, comprising the following steps:

[0033] S1. Discretize the geometry of the MOS device into a three-dimensional cellular mesh, and define a state vector containing multiphysics information for each cell in the three-dimensional cellular mesh.

[0034] The state vector includes at least: carrier density and local potential for characterizing electrical properties, average carrier energy for characterizing quantum effects, local temperature for characterizing thermal effects, and defect states for characterizing reliability effects; to simulate the process variability of the device, the initial defect states of each cell in the three-dimensional cellular grid are randomized when defining the state vector.

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

[0036] The geometry of a MOS device refers to its complete internal and external three-dimensional spatial structure, including the spatial layout, dimensions, and interfaces between all its components.

[0037] First, based on the given three-dimensional geometry of the MOS device to be modeled, its continuous physical space is discretized into a three-dimensional cellular mesh. The grid consists of a large number of closely adjacent cells. Composition, in which A unique index for each cell. Each cell... Each cell is assigned material properties to distinguish it from other regions, such as semiconductors, insulators, or conductors. The size of the cells can be set according to the simulation accuracy requirements, achieving a balance between computational resources and physical detail description.

[0038] After completing the geometric discretization, each cell in the 3D cellular mesh is... Defined at discrete time points state vector This state vector aims to intrinsically contain the core information required for multi-physics coupling effects within the device through a unified data structure. The definition of this state vector forms the basis for all subsequent evolution calculations in this invention. Its specific structure can be represented by the following formula:

[0039] ;

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

[0041] Carrier density and local potential It is a core component used to characterize the basic electrical properties within a unit cell. This represents the concentration of free carriers within the cell, while This describes the potential level at that point.

[0042] To describe quantum effects, the state vector contains the average energy of the charge carriers. In nanoscale MOS devices, the energy state of charge carriers deviates significantly from equilibrium due to quantum confinement effects and high-field transport. Treating the average energy of charge carriers as an independent state variable allows subsequent evolution rules to take the energy state of charge carriers as input, thereby indirectly accounting for the effects of hot carrier effects and partial quantum tunneling effects on device performance.

[0043] To describe the thermal effect, the state vector includes the local temperature. This component is used to characterize the cell. The lattice temperature. Devices using advanced processes exhibit significant self-heating effects due to their high power density. Incorporating the local temperature into the state vector allows subsequent evolution to account for the conduction of Joule heat generated within the device, thereby achieving bidirectional coupling modeling between electrothermal processes.

[0044] To describe the reliability effect, the state vector includes defect states. This component is a set used to record the cells in detail. The physical properties of various point defects present internally and their current charge occupancy states are analyzed. By simulating the trapping and emission of charge carriers by defects in subsequent evolution, reliability degradation phenomena such as bias temperature instability and hot carrier injection can be modeled.

[0045] In modeling reliability degradation processes with memory effects, the state vector also includes historical path states. The historical path state is used to record the evolution trajectory of the defect state over multiple discrete time steps, thereby enabling the modeling of non-Markovian effects in device reliability. This component is a data structure, a first-in-first-out queue, used to store the defect state. The evolution trajectory over several discrete time steps. When calculating certain evolution probabilities related to defects, one can consider not only the current system state but also its recent historical states.

[0046] After defining the structure of the state vector, it needs to be initialized, that is, set... The initial state of the system at time t. To simulate the inherent process variability of the device, the initial defect state of each cell in the three-dimensional cellular mesh is defined when defining the state vector. Perform randomization settings. For cells. It independently generates a set of initial defect instances that conform to the above statistical laws, including the number of defects, their spatial location, and the initial charge occupancy state of the energy levels. It can generate a large number of device instances that differ in microscopic defect distribution but conform to the same process characteristics in macroscopic statistics, thus providing input for subsequent statistical fluctuation analysis of the devices.

[0047] S2. The dynamic behavior of the device is simulated by iteratively updating the state vector of each cell within discrete time steps. This iterative update is achieved through a two-layer adaptive evolution rule system, which includes a meta-learning rule layer and a basic rule layer.

[0048] By utilizing a meta-learning rule layer, a set of basic rule parameters in the basic rule layer corresponding to each cell is dynamically adjusted based on the local macroscopic state within the neighborhood of each cell; preferably, this includes:

[0049] Calculate the average value of the state vector components in the neighborhood of each cell to obtain the local macroscopic state;

[0050] Then, the basic rule parameter set is updated according to the local macroscopic state using a preset mapping function.

[0051] Using the basic rule layer, the evolution of the state vector in discrete time is calculated using the basic rule parameter set adjusted by the meta-learning rule layer; preferably, it also includes: updating the local potential: the update is based on the discrete form of the Poisson equation, and the local potential of the cell is updated according to the carrier density in each cell and its neighborhood and the net charge density determined by the defect state.

[0052] The established two-layer adaptive evolution rule system is a hierarchical computational structure. The upper layer (meta-learning rule layer) dynamically adjusts the computational parameters based on the local state of the system, while the lower layer (basic rule layer) uses these adjusted parameters to specifically execute the evolutionary calculation of the system state. The meta-learning rule layer is the computational level, whose function is to dynamically adjust and output a set of physical parameters for the basic rule layer to use for specific evolutionary calculations based on the local macroscopic state of the system. The basic rule layer is the computational level, whose function is to use the dynamically adjusted set of basic rule parameters provided by the meta-learning rule layer to specifically execute the evolutionary calculation of the state vector from the current time step to the next time step. The local macroscopic state is a physical quantity used to characterize the local physical environment of a cell, such as the local average carrier energy, local electric field gradient, or local temperature, obtained by spatially processing the state vector components of a cell and its neighboring cells.

[0053] In this embodiment, step S2 is the core execution step for simulating the dynamic behavior of the MOS device. This step is performed at discrete time steps. Internally, through a two-layer adaptive evolution rule system, the state vectors of all cells defined in step S1 are... Perform iterative updates to obtain the state at the next time step. .

[0054] The two-layer adaptive evolution rule system includes a meta-learning rule layer and a basic rule layer, which work together sequentially in each time step.

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

[0056] Specifically, for cells The meta-learning rule layer first calculates its neighborhood. Local macroscopic state within The local macroscopic state is a scalar or vector obtained by spatial averaging of the state vector components of the cells in the neighborhood, and is used to characterize the local physical environment in which the cell is located.

[0057] Then, the meta-learning rule layer uses a pre-defined mapping function. Based on the newly obtained local macroscopic state To dynamically adjust and output the cell The set of basic rule parameters to be used in the next time step The update process can be described by the following formula:

[0058] ;

[0059] in, For cell indexing, For the current time step, For time step. This is a pre-defined mapping function, determined before modeling begins; it can be an analytical function or a lookup table. As input, cells In time The local macroscopic state. These are a fixed, global set of meta-parameters used to calibrate the mapping function. The specific form of.

[0060] Basic rule parameter set It is a set of multiple key physical parameters. This set includes at least one of the following: carrier mobility, which determines the drift and diffusion behavior of carriers; scattering rate, which describes the energy relaxation process of high-energy carriers; material thermal conductivity, which describes the lattice thermal conductivity; and defect trapping cross section, which describes the defect trapping emission dynamics.

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

[0062] The core of the computation for the evolution of the electrical and quantum-related components in the state vector lies in determining the cell. Its neighboring cells carrier transition probabilities The probability is calculated based on the local potential difference between adjacent cells. and the average energy difference of charge carriers It directly calls the set of basic rule parameters provided by the meta-learning rule layer. The transport-related parameters in the data. The dependency relationship of this calculation can be expressed as:

[0063] ;

[0064] in, It is a transition function that describes the specific physical mechanism of a transition, and its internal parameters are all determined by... Provided. Through cells By calculating the transition probabilities between the carrier and all its neighbors, the net carrier flux can be obtained, thereby updating the carrier density. The average carrier energy is updated based on the energy gain or loss during transport. .

[0065] To ensure the self-consistency of the potential distribution, the evolution of the state vector in discrete time is calculated using a basic rule layer, which also includes updating the local potential. Based on the current carrier density within each cell and its neighborhood. and defect status The net charge density, which is jointly determined, is used to solve for a new potential distribution that matches this charge distribution. .

[0066] For thermal components The evolution of the state vector is calculated using the basic rule layer, which also includes updating the local temperature. This update is based on the temperature gradient between cells to calculate the heat flux, while incorporating Joule heat generated by the resistance effect during carrier transport as a source term. The thermal conductivity required for calculating the heat flux is also a parameter dynamically adjusted by the meta-learning rule layer based on the local state.

[0067] Through the above series of calculations, the state vectors of all cells were transformed from... arrive This is one complete iteration. This process will be repeated throughout the entire simulation duration.

[0068] S3. After iterative update, extract the macroscopic electrical characteristics of the MOS device based on the obtained cell state vector.

[0069] In this embodiment, step S3, after the iterative evolution process in step S2 is completed, involves processing and analyzing the obtained set of full device cell state vectors containing rich microscopic physical information to extract key parameters that characterize the macroscopic electrical properties of the MOS device. This step serves as a bridge connecting microscopic physical simulation and macroscopic device performance characterization.

[0070] Specifically, this step begins after the iterative update reaches a steady-state condition or reaches a preset simulation duration.

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

[0072] First, it is necessary to identify the sets of cells that constitute the various electrodes of the device from the three-dimensional cellular mesh. These cells are typically boundary cells with conductor material properties that are connected to an external voltage source.

[0073] Then, taking the calculation of 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 are not part of the drain electrode. In each iteration of step S2, the carrier transition probabilities and net flux between all adjacent cells have actually been calculated. Therefore, when extracting macroscopic characteristics, it is only necessary to sum these microscopic fluxes. Drain current The calculation can be described by the following formula:

[0074]

[0075] in, This is the set of cells representing the drain electrode. Summation is performed by iterating through all drain cells. The second summation involves traversing the cells. All neighbors In the middle, those cells that do not belong to the drain electrode. It is in time From cell Flow to cells The net carrier flux. This represents the fundamental charge. It integrates the flow of microscopic charge carriers across the entire drain channel interface into a macroscopic endpoint current.

[0076] It should be understood that a single execution of steps S1 to S3 only yields the device response under a single combination of external bias voltages. To obtain the complete characteristic curve of the device, it is necessary to repeatedly execute the complete steps S2 to S3 under different combinations of external bias voltages, i.e., to perform a voltage scan. The curve can fix the drain voltage and then scan the gate voltage with a certain step size to perform a complete dynamic evolution and characteristic extraction process on the gate voltage point, and finally connect the data of all scan points into a line.

[0077] Furthermore, the state vector defined in this invention also supports the extraction of other macroscopic electrical properties. The total charge in the gate electrode cell set can be calculated. With gate voltage The rate of change is used to extract the gate capacitance characteristics of the device.

[0078] It enables macroscopic characterization of device reliability and variability. By simulating the changes in macroscopic characteristics of a device before and after experiencing prolonged electrical or thermal stress, the degree of degradation and threshold voltage drift can be quantified. Regarding variability, since a large number of device instances with different microscopic defect distributions are generated in step S1, the complete S1 to S3 process can be executed on the instances to obtain the statistical distribution of macroscopic parameters. This statistical distribution intuitively reflects the fluctuations in macroscopic device performance caused by microscopic randomness.

[0079] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A modeling method for a MOS device, characterized in that, include: S1. Discretize the geometry of the MOS device into a three-dimensional cellular mesh, and define a state vector containing multiphysics information for each cell in the three-dimensional cellular mesh. The state vector includes at least: carrier density and local potential for characterizing electrical properties, average carrier energy for characterizing quantum effects, local temperature for characterizing thermal effects, and defect states for characterizing reliability effects; and, to simulate the process variability of the device, the initial defect states of each cell in the three-dimensional cellular grid are randomized when defining the state vector. S2. The dynamic behavior of the device is simulated by iteratively updating the state vector of each cell within discrete time steps, wherein the iterative update is implemented through a two-layer adaptive evolution rule system, which includes a meta-learning rule layer and a basic rule layer: By utilizing the meta-learning rule layer, a set of basic rule parameters in the basic rule layer corresponding to each cell is dynamically adjusted based on the local macro-state in the neighborhood of each cell. Using the basic rule layer and the basic rule parameter set adjusted by the meta-learning rule layer, the evolution of the state vector in discrete time is calculated; S3. After the iterative update, the macroscopic electrical characteristics of the MOS device are extracted based on the obtained cell state vector.

2. The modeling method for a MOS device according to claim 1, characterized in that, In S2, a meta-learning rule layer is used to dynamically adjust a set of basic rule parameters in the basic rule layer corresponding to each cell based on the local macro-state in the neighborhood of each cell. Specifically, this includes: Calculate the average value of the state vector components in the neighborhood of each cell to obtain the local macroscopic state; Then, the basic rule parameter set is updated according to the local macroscopic state using a preset mapping function.

3. The modeling method for a MOS device according to claim 2, characterized in that, The set of basic rule parameters includes at least one of the following: carrier mobility, scattering rate, thermal conductivity, and defect trapping cross section.

4. The modeling method for a MOS device according to claim 2, characterized in that, The basic rule parameter set The update is achieved through the following formula: ； in, For cell indexing, For the current time step, For time step, For the preset mapping function, For cells In time The aforementioned local macroscopic state, It is a fixed set of global meta-parameters.

5. The modeling method for a MOS device according to claim 1, characterized in that, In S2, using the basic rule layer and the basic rule parameter set adjusted by the meta-learning rule layer, the evolution of the state vector in discrete time is calculated, including: calculating carrier transport between cells. Based on the difference between the local potential and the average energy of the charge carriers between adjacent cells, and using the transport-related parameters in the basic rule parameter set, the carrier transition probability between cells is calculated.

6. The modeling method for a MOS device according to claim 5, characterized in that, From cell to adjacent cells carrier transition probability The computation includes the following dependencies: ； in, For transition functions, For cells and The local potential difference between them For cells and The difference in average carrier energy between them This refers to the set of basic rule parameters in S2 after being adjusted by the meta-learning rule layer.

7. The modeling method for a MOS device according to claim 1, characterized in that, S2 utilizes a basic rule layer and uses the basic rule parameter set adjusted by the meta-learning rule layer to calculate the evolution of the state vector in discrete time. It also includes updating the local potential: This update is based on the discrete form of the Poisson equation and updates the local potential of the cell according to the carrier density in each cell and its neighborhood and the net charge density determined by the defect state.

8. The modeling method for a MOS device according to claim 1, characterized in that, S2 utilizes a basic rule layer and uses the basic rule parameter set adjusted by the meta-learning rule layer to calculate the evolution of the state vector in discrete time. It 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 modeling method for a MOS device according to claim 1, characterized in that, The state vector in S1 also includes historical path states, which are used to record the evolution trajectory of the defect state over multiple discrete time steps in the past, so as to model the non-Markovian effects in device reliability.

10. The modeling method for a MOS device according to claim 1, characterized in that, The extraction of the macroscopic electrical characteristics of the MOS device described in S3 specifically includes: calculating the terminal current of the MOS device by integrating the net carrier flux through the boundary cells representing the device electrodes.

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