Electronic product performance prediction and optimization system

Abstract

The invention discloses an electronic product performance prediction and optimization system, and relates to the technical field of data analysis and processing. The system comprises a performance analysis part, a performance prediction part and a performance optimization control part. The performance analysis part is used for acquiring product performance parameters of a target electronic product and calculating power consumption density by acquiring electric field distribution of the target electronic product in real time; the performance prediction part is used for taking the carrier concentration distribution, the hot carrier energy spectrum and the power consumption density as a performance prediction result; and the performance optimization control part is used for constructing a multi-target optimization equation of the target electronic product based on the carrier concentration distribution, the hot carrier energy spectrum and the reliability index, and obtaining the optimal control voltage and the optimal control frequency by solving the optimization equation. According to the method, the performance of the electronic product is accurately predicted, and the control voltage and frequency are dynamically adjusted in combination with a multi-factor optimization strategy, so that the comprehensive optimization of the product performance is realized.

Description

Technical Field

[0001] The present disclosure relates to, but is not limited to, the field of data analysis and processing technology, and in particular to an electronic product performance prediction and optimization system. Background Art

[0002] Traditional electronic product performance optimization usually adopts optimization methods based on a single goal, such as power consumption optimization, thermal effect control or reliability improvement. These optimization technologies are designed for a specific performance goal, and common methods include low-power design, electric field or current control, thermal management technology, reliability prediction model, etc. For example, power consumption optimization technology usually uses means such as reducing voltage or reducing current to directly reduce power consumption density, but this may cause the performance of electronic products to decline or the response speed to slow down. In thermal effect control technology, heat conduction materials, heat sinks or fans are usually used to reduce the problem of local overheating. However, this type of thermal management method often simply controls the temperature, but fails to optimize the generation and distribution of hot carrier energy from the perspective of electric field distribution and carrier behavior.

[0003] Among existing optimization technologies, the biggest drawback of single-objective optimization is that it fails to fully consider the complex relationships between various performance factors. For example, while reducing power consumption, it may have a negative impact on the overall reliability of electronic products; when performing thermal management, if the temperature rise is excessively restricted, the resistance of the material may increase, resulting in increased power consumption. In addition, existing technologies generally lack multi-objective comprehensive optimization methods and fail to find a reasonable balance between multiple objectives such as power consumption, temperature and reliability. Failures in modern electronic products are often the result of the combined effects of multiple factors. Therefore, if the correlation between the factors is ignored, the optimization effect may be greatly reduced.

[0004] Although the existing technology has achieved certain results in single-objective performance optimization, there are still some major problems that have not been solved: Limitations of multi-objective optimization methods: Most of the existing optimization technologies are based on a single objective, such as power consumption optimization, thermal effect control or reliability improvement. However, the design and optimization of electronic products involve multiple interrelated performance indicators, such as power consumption, temperature and reliability. There is often a mutually restrictive relationship between these performance indicators. In the process of optimizing one goal, it is easy to ignore the impact on other goals. For example, simply reducing power consumption may slow down the movement of carriers, thereby reducing overall performance; while excessively increasing the intensity of power density control may cause an increase in thermal effects, which in turn affects the reliability of the material. Lack of accurate modeling of dynamic changes: Existing optimization methods usually rely on static models or simple models of a single factor, and fail to fully consider the dynamic changes of electronic products under complex working conditions. For example, under dynamic working conditions, changes in electric field strength, generation and scattering behavior of hot carriers, and real-time changes in carrier concentration will have a significant impact on the overall performance of the product. These dynamic changes are often difficult to accurately capture by existing models, so the prediction and optimization effects of existing technologies are limited. Summary of the invention

[0005] The present disclosure provides an electronic product performance prediction and optimization system, which achieves a more accurate prediction of the performance of the electronic product, and combines a multi-factor optimization strategy to dynamically adjust the control voltage and frequency to achieve all-round optimization of the electronic product performance.

[0006] In order to solve the above problems, the technical solution of the present invention is achieved as follows:

[0007] An electronic product performance prediction and optimization system, the system comprising: a performance analysis part, a performance prediction part and a performance optimization control part; the performance analysis part is used to obtain product performance parameters of a target electronic product, calculate the carrier concentration distribution of the target electronic product by real-time acquisition of the electric field distribution of the target electronic product; calculate the hot carrier energy spectrum of the target electronic product based on the carrier concentration distribution; calculate the power consumption density based on the hot carrier energy spectrum of the target electronic product; the performance prediction part is used to calculate the reliability index of the target electronic product as a result of performance prediction based on the carrier concentration distribution, the hot carrier energy spectrum and the power consumption density; the performance optimization control part is used to construct a multi-objective optimization equation for the target electronic product based on the carrier concentration distribution, the hot carrier energy spectrum and the reliability index, and obtain the optimal control voltage and the optimal control frequency by solving the optimization equation.

[0008] Furthermore, product performance parameters of the target electronic products include: carrier mobility, effective state density, Fermi level, carrier scattering rate, electrical conductivity, maximum allowable temperature, maximum power consumption density, maximum carrier concentration and maximum hot carrier density.

[0009] Furthermore, the carrier concentration distribution of the target electronic product is calculated by the following formula:

[0010]

[0011] Where n(r, t) is the carrier concentration distribution of the target electronic product at position r at time t; D n is the diffusion coefficient of carriers; μ n is the carrier mobility; E(r, t) is the electric field strength when the target electronic product is at position r at time t; G(r, t) is the carrier generation rate when the target electronic product is at position r at time t.

[0012] Furthermore, the hot carrier energy spectrum of the target electronic product is calculated by the following formula:

[0013]

[0014] Where φ(E, r, t) represents the density of hot carriers with energy E at position r and time t; N C is the effective state density, which represents the available state density of the conduction band in the semiconductor material; E represents the energy of the carrier; E F is the Fermi level, which represents the energy level benchmark in semiconductor materials; k B is the Boltzmann constant; T is the temperature; q is the charge, which indicates the charge size of the carrier; λ is the mean free path, which indicates the average movement distance of the carrier between two scatterings; S is the carrier scattering rate.

[0015] Furthermore, the power consumption density is calculated by the following formula:

[0016]

[0017] Among them, P local (r, t) is the power consumption density, which represents the power consumption caused by the movement of carriers in the material at position r and time t; σ(n, T) is the conductivity, which represents the conductivity of the material at carrier concentration n and temperature T.

[0018] Furthermore, the reliability index of the target electronic product is calculated by the following formula:

[0019]

[0020] Among them, R(t) is the reliability index, which indicates the reliability of the target electronic product at time t. The closer R(t) is to 1, the higher the stability of the target electronic product is, and the closer it is to 0, the greater the probability of failure of the target electronic product is. τ is the time integral variable; P local (r, τ) represents the power consumption density at position r and time τ; P crit (T) is the critical power consumption density, which indicates the maximum power consumption density that the target electronic product can withstand at temperature T; n(r,τ) indicates the carrier concentration at position r and time τ; n max (T) is the maximum carrier concentration, which indicates the maximum carrier concentration that the target electronic product can withstand at temperature T;

[0021] Φ(E m ,r,τ) means at position r, time τ and energy E m The density of hot carriers under m represents the average energy; Φ th (T) is the hot carrier threshold, which indicates the maximum hot carrier density that the target electronic product can withstand at temperature T; Ω represents the spatial area of ​​the entire target electronic product, which is integrated to obtain the global damage distribution.

[0022] Furthermore, the multi-objective optimization equation of the target electronic product is expressed by the following formula:

[0023] min V,f {α 1 ∫ Ω P local (r,t)dΩ+α 2 max Ω [T]-α 3 R(t)};

[0024] Satisfy the constraints:

[0025]

[0026] Among them, V is voltage, f is frequency, both of which are control variables of the multi-objective optimization equation. By solving the multi-objective optimization equation, the optimal control voltage and optimal control frequency are obtained; α 1 , α 2 and α 3 are all preset weight parameters; ∫ Ω P local (r,t)dΩ represents the global power consumption of the entire target electronic product; max Ω [T] is the maximum temperature, which indicates the highest temperature inside the target electronic product; T max R is the maximum allowable temperature of the target electronic product, which is used to limit the temperature not exceeding the failure point of the material;min : Minimum reliability threshold.

[0027] Furthermore, α 1 The value range of α is 0.2 to 0.5; 2 The value range of α is 0.1 to 0.3; 3 The value range is 0.4 to 0.7; and it satisfies:

[0028] α 1 +α 2 +α 3 =1.

[0029] The electronic product performance prediction and optimization system of the present invention has the following beneficial effects: the present invention realizes the comprehensive optimization of the performance of electronic products by constructing a multi-objective optimization equation. This optimization equation not only takes into account the minimization of global power consumption, but also controls the maximum temperature inside the product within a safe range, and evaluates the long-term stability of the product by introducing a reliability index. Different from the single optimization target method commonly used in the prior art, the optimization method of the present invention can find a reasonable balance between power consumption, temperature and reliability. Through this comprehensive optimization method, the system effectively controls the temperature rise while reducing power consumption, and ensures the reliability of the product. Therefore, the electronic products show higher stability and energy efficiency in long-term operation, greatly reducing the risk of failure and the possibility of thermal failure. The present invention adopts dynamic modeling technology, which can track the carrier concentration distribution, electric field distribution and hot carrier energy spectrum inside the electronic product in real time. The core of this dynamic modeling technology is that it can accurately describe the movement of carriers in materials and energy state changes through mathematical tools such as partial differential equations and probability distribution. Through real-time monitoring of these dynamic factors, the system can adjust the optimization strategy in time so that the voltage and frequency are always within the optimal range under different working conditions. Compared with the traditional static modeling method, the dynamic modeling technology of the present invention can better cope with the performance fluctuations of electronic products under complex working conditions, and ensure that the optimization results are always efficient and stable under different environmental conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A schematic diagram of the system structure of an electronic product performance prediction and optimization system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present disclosure clearer and more understandable, the present disclosure is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present disclosure and are not used to limit the present disclosure.

[0032] Example 1, reference Figure 1 : An electronic product performance prediction and optimization system, the system comprising: a performance analysis part, a performance prediction part and a performance optimization control part; the performance analysis part is used to obtain product performance parameters of a target electronic product, and calculate the carrier concentration distribution of the target electronic product by real-time acquisition of the electric field distribution of the target electronic product; based on the carrier concentration distribution, the hot carrier energy spectrum of the target electronic product is calculated; based on the hot carrier energy spectrum of the target electronic product, the power consumption density is calculated; the performance prediction part is used to calculate the reliability index of the target electronic product as a result of performance prediction based on the carrier concentration distribution, the hot carrier energy spectrum and the power consumption density; the performance optimization control part is used to construct a multi-objective optimization equation for the target electronic product based on the carrier concentration distribution, the hot carrier energy spectrum and the reliability index, and obtain the optimal control voltage and the optimal control frequency by solving the optimization equation.

[0033] Specifically, first of all, the basic work of the performance analysis part is to collect the electric field distribution of the target electronic product in real time. The collection of electric field distribution is the first step of the system, and its purpose is to grasp the changes in the electric field inside the electronic product. The electric field distribution inside the electronic product will be affected by many factors, such as external voltage, conductivity of the material inside the product, geometric structure, etc. Since the electric field plays a direct driving role in the movement of electrons and holes, the change of the electric field distribution will directly affect the flow and concentration distribution of carriers. Through sensors and signal acquisition equipment, the system can obtain the electric field data inside the electronic product in real time. In order to describe the electric field distribution more accurately, the system may adopt multi-point or multi-dimensional collection methods to obtain higher resolution electric field information. This information is not only the basic data for performance analysis, but also provides the necessary input for subsequent carrier concentration calculations. Based on the collected electric field data, the system further calculates the carrier concentration distribution inside the target electronic product. The distribution of carrier concentration determines the current transmission characteristics in the electronic product and is one of the key parameters reflecting the performance of the electronic product. The basic principle is that under the action of the electric field, carriers (electrons and holes) will migrate in the semiconductor material and form a certain concentration distribution. By combining the electric field distribution with the physical properties of the material, the system can derive the carrier concentration distribution function. This process usually involves modeling the relationship between the electric field and the material parameters, and differential equations may be used to characterize the effect of the electric field on the movement of carriers. Changes in carrier concentration directly affect the electrical properties of electronic products, such as changes in conductivity and resistivity. Therefore, by accurately calculating the carrier concentration distribution, the system can effectively capture the electrical behavior of electronic products under different working conditions, laying the foundation for subsequent energy spectrum analysis and power consumption calculation.

[0034] After calculating the carrier concentration distribution, the system further constructs the hot carrier energy spectrum of the target electronic product. The so-called hot carrier energy spectrum refers to the distribution of energy states generated by the thermal motion of carriers inside the electronic product. For high-performance electronic products, the influence of thermal effects on carrier motion cannot be ignored. Under the action of an external electric field, carriers not only migrate in space, but also obtain different energy states due to thermal excitation. The distribution of these energy states is called the hot carrier energy spectrum. The basic principle of the hot carrier energy spectrum is that the distribution of carriers in a specific energy state can be described by a comprehensive analysis of the carrier concentration and temperature field. This analysis process may involve solving the thermal equilibrium state of the carriers and statistically modeling the probability density of carriers in different energy states. The hot carrier energy spectrum not only reflects the activeness of the carrier movement in the material, but also provides important reference information for subsequent power consumption analysis. Based on the hot carrier energy spectrum, the system further calculates the power consumption density of the target electronic product. Power consumption density is a key indicator to measure the energy consumption of electronic products during operation. It reflects the energy utilization efficiency of the product and the internal thermal management status. The system derives the distribution of power consumption density by accurately calculating the energy state of hot carriers. The basic principle is that the movement speed and collision frequency of carriers will change under different energy states, and these changes will lead to different power consumption. Therefore, the calculation of power consumption density usually needs to consider the energy loss of carriers under different energy states and the relationship between these losses and the electric field strength and material conductivity. The calculation formula of power consumption density is essentially a manifestation of the law of conservation of energy. By accurately modeling the flow of energy, the system can identify high-energy consumption areas of electronic products under different working conditions. The calculation results of power consumption density are not only used to evaluate the energy efficiency of electronic products, but also provide a specific quantitative basis for subsequent performance optimization.

[0035] In principle, the performance analysis part can fully reveal the performance changes of electronic products under different working conditions through comprehensive analysis of multi-dimensional physical quantities. Compared with the existing technology, the uniqueness of this system is that it not only focuses on a single electric field distribution or temperature distribution, but also realizes a comprehensive characterization of the performance of electronic products through the joint analysis of multiple parameters such as carrier concentration, hot carrier energy spectrum and power consumption density. The existing technology can usually only analyze a single performance parameter, while this system can more accurately predict the working state and performance changes of electronic products in complex environments through comprehensive calculation of multiple parameters. This multi-dimensional performance analysis method provides an innovative solution for the refined management and optimization of electronic products. The performance analysis part of the electronic product performance prediction and optimization system constructs a multi-dimensional model reflecting carrier concentration, hot carrier energy state and power consumption density by accurately collecting the electric field distribution of the target electronic product. The electric field distribution is the basis of the carrier concentration distribution, and the change of carrier concentration directly affects the construction of the hot carrier energy spectrum. Finally, the calculation of the hot carrier energy spectrum provides key data support for the analysis of power consumption density. This interlocking analysis process not only reveals the complex electrical and thermal behavior inside electronic products, but also lays a solid foundation for subsequent performance prediction and optimization control. These innovative analysis methods in the performance analysis part overcome the limitations of single parameter analysis in existing technologies by introducing multi-dimensional physical parameters, allowing the system to evaluate the performance of electronic products more comprehensively and accurately.

[0036] Carrier concentration is a basic physical quantity that describes the dynamic distribution of electrons and holes in semiconductor materials. The number and distribution of carriers directly affect the conductivity and energy transfer characteristics of the material. Therefore, it is one of the core indicators for measuring the performance of electronic products. In the prediction model, the carrier concentration distribution is not only an important representation of the current working state of the electronic product, but also provides the necessary input data for the system to analyze the energy changes during the carrier migration process. By modeling the carrier concentration at different locations, the system can capture the flow characteristics of carriers in different energy states, thereby more accurately describing the electric field and current changes inside the electronic product.

[0037] Secondly, the performance prediction part further analyzes the energy state distribution of carriers through the hot carrier energy spectrum. The hot carrier energy spectrum reflects the distribution of carriers between different energy states under the action of thermal motion. For electronic products, the presence of hot carriers has a significant impact on the performance and reliability of the product. Especially in high temperature or high frequency environments, thermal effects may lead to enhanced carrier migration, which in turn causes energy loss and local temperature rise of the material. By modeling the hot carrier energy spectrum, the system can fully understand the energy state distribution of carriers and incorporate it as an input parameter into the performance prediction model. This energy distribution-based analysis method enables the system to better reflect the motion characteristics of carriers in complex environments, thereby providing more accurate data support for reliability prediction. Furthermore, the performance prediction part also uses power consumption density as one of the key input parameters. Power consumption density reflects the energy consumption of electronic products under different working conditions and is an important indicator for measuring product energy utilization efficiency and thermal management effects. Changes in power consumption directly affect the operating temperature of electronic products, and the increase in temperature will in turn affect the migration and thermal excitation process of carriers. Therefore, power consumption density is not only a measure of product performance, but also an important factor affecting its reliability. The performance prediction part constructs a multi-factor reliability evaluation model by comprehensively analyzing the power consumption density, carrier concentration and energy spectrum. This model starts from multiple dimensions, combines carrier concentration, energy state and power consumption, and obtains a comprehensive reliability index by analyzing the interaction between various factors. In the process of building the reliability model, the performance prediction part particularly emphasizes the dynamic correlation between various parameters. Specifically, the carrier concentration distribution reflects the electrical characteristics inside the electronic product, the hot carrier energy spectrum reveals the distribution of carriers under different energy states, and the power consumption density reflects the thermal effect of the product during energy consumption. By comprehensively analyzing these parameters, the system can establish a more accurate prediction model. This model can not only accurately capture the performance changes of the product under different working conditions, but also predict the possible failure of the product under extreme conditions. Unlike the traditional single-parameter prediction method, the performance prediction part of the present invention makes the reliability prediction more comprehensive and accurate through multi-dimensional and multi-factor comprehensive modeling.

[0038] The performance optimization control part first takes the reliability index obtained from the performance prediction part as input and combines it with the carrier concentration distribution and hot carrier energy spectrum obtained from the previous analysis. The reliability index is not just a single measurement standard here, it directly reflects the failure risk and performance changes of electronic products under different working conditions. Therefore, when building the optimization model, the reliability index is regarded as a key reference parameter. At the same time, the carrier concentration distribution and hot carrier energy spectrum provide detailed physical information about the internal state of the electronic product. This information contains the electrical and thermal characteristics exhibited by the electronic product during operation, thus providing comprehensive input data for multi-objective optimization. In order to achieve performance optimization, the system constructs a multi-objective optimization model based on these input data. The core idea of ​​the optimization model is to mathematically express multiple performance objectives of the electronic product, and then solve them through the optimization algorithm to find the best control solution. In this process, the multi-objective optimization equation comprehensively considers the control voltage, control frequency, and related reliability and power consumption constraints. As the main control parameters of electronic products, the control voltage and control frequency directly affect the migration speed of carriers, current density, and the intensity of thermal effects. Therefore, in the process of constructing the optimization equation, these parameters need to be accurately modeled to ensure that the final optimization results can comprehensively improve the performance of electronic products.

[0039] In the process of solving the optimization equation, the system usually adopts an advanced optimization algorithm, such as genetic algorithm or particle swarm algorithm. These algorithms can perform global search in multi-dimensional parameter space to find the optimal control solution. Through this global search method, the system can select the optimal solution from a large number of candidate solutions, avoiding the dilemma of local optimality in traditional optimization methods. At the same time, the performance optimization control part also takes into account the dynamic characteristics of electronic products under different working conditions. By introducing a dynamic feedback mechanism, the system can monitor the performance changes of electronic products in real time in actual applications and adjust the weights and constraints in the optimization model according to the changes. This dynamic feedback mechanism enables the system to maintain high adaptability and stability in a complex working environment, thereby further improving the accuracy of optimization control. It is worth mentioning that the performance optimization control part not only focuses on the overall performance of the product, but also takes into account the balance between energy efficiency and reliability. In many high-performance electronic products, the pursuit of higher computing speed or stronger functions is often accompanied by an increase in energy consumption and an increase in reliability risks. Therefore, in the construction of the optimization model, the system adopts a multi-objective trade-off strategy, which comprehensively optimizes energy efficiency, reliability and performance improvement as different goals. Through this strategy, the system can achieve the optimal balance between energy efficiency and performance while ensuring reliability. The innovation of this optimization strategy lies in that, through dynamic adjustment of various performance objectives, the optimization model can adapt to different application scenarios and needs, thereby providing personalized optimization solutions.

[0040] Embodiment 2: The product performance parameters of the target electronic product include: carrier mobility, effective state density, Fermi level, carrier scattering rate, electrical conductivity, maximum allowable temperature, maximum power consumption density, maximum carrier concentration and maximum hot carrier density.

[0041] Specifically, carrier mobility, as a parameter describing the motion characteristics of electrons and holes in materials, directly reflects the response speed of carriers under the action of an external electric field. The higher the mobility, the stronger the mobility of carriers in the material, which affects the conductivity of the material. In optimization control, carrier mobility can serve as a bridge between electric field distribution and carrier behavior to determine the mobility efficiency of carriers and the overall conductivity of the material. Through dynamic analysis of mobility, the system can accurately evaluate the changes in the conductivity of electronic products under different working conditions and provide a strong basis for optimization control. The effective state density refers to the number of effective quantum states of carriers in semiconductor materials, which depends on the energy band structure of the material. The effective state density reflects the number of energy levels in the material that can be occupied by carriers within a specific energy range. This parameter is crucial for the performance analysis of electronic products because it directly affects the distribution and concentration of carriers in the material. By modeling the effective state density, the system can further deduce the distribution state of carriers and provide accurate data support for subsequent energy spectrum analysis.

[0042] The Fermi level is a key parameter that describes the energy state of carriers. It reflects the distribution of electrons and holes in the material under thermal equilibrium. Changes in the Fermi level will directly affect the electrical properties of the material, so the setting of the Fermi level is particularly important in performance prediction. The system can flexibly adapt to different working environments and conditions by dynamically adjusting the Fermi level, thereby improving the accuracy of the prediction model. The carrier scattering rate describes the probability of scattering of carriers due to defects or impurities when they move in the material. The scattering process affects the mobility and energy loss of the carriers, so the carrier scattering rate directly affects the performance and power consumption of electronic products. In optimization control, the system can reduce the energy loss of carriers by adjusting the scattering rate, thereby improving the energy efficiency of electronic products.

[0043] As a parameter reflecting the conductive properties of materials, conductivity directly determines the current transmission capacity of electronic products. Conductivity is closely related to carrier concentration and mobility. Therefore, in performance prediction and optimization control, the precise setting of conductivity is crucial. Through dynamic adjustment of conductivity, the system can effectively control the current distribution and power utilization efficiency of electronic products. The maximum allowable temperature refers to the highest temperature that electronic products can withstand during operation. High temperature often leads to enhanced carrier excitation and may cause thermal failure of materials. Therefore, in performance prediction and optimization, the system needs to monitor the operating temperature of electronic products in real time to ensure that it does not exceed the maximum allowable temperature, so as to avoid performance degradation and failure caused by overheating. The maximum power consumption density reflects the maximum energy consumption of electronic products under specific conditions. This parameter directly affects the thermal management and energy efficiency of electronic products. Therefore, in optimization control, the maximum power consumption density is a constraint that needs to be considered. Through strict control of the maximum power consumption density, the system can improve the energy efficiency of electronic products and reduce the risk of thermal failure while ensuring performance. The maximum carrier concentration and the maximum hot carrier density are important parameters for describing the carrier and thermal excitation states in materials. Their settings directly affect the current transmission characteristics and thermal excitation effects of electronic products. In the optimization control, the system can effectively adjust the working state of electronic products by real-time monitoring of these two parameters to ensure that they are always in an efficient and stable working range.

[0044] Embodiment 3: Calculate the carrier concentration distribution of the target electronic product by the following formula:

[0045]

[0046] Where n(r, t) is the carrier concentration distribution of the target electronic product at position r at time t; D n is the diffusion coefficient of carriers; μ n is the carrier mobility; E(r, t) is the electric field strength when the target electronic product is at position r at time t; G(r, t) is the carrier generation rate when the target electronic product is at position r at time t.

[0047] Specifically, the left side of the equation It represents the rate of change of carrier concentration at any position r and time t. This is a time derivative that reveals the trend of carrier concentration over time. Inside electronic products, due to the combined influence of multiple factors, the carrier concentration is not constant over time, but is constantly adjusted with changes in electric field, diffusion process and external excitation. Therefore, this time derivative provides us with a key indicator to measure how the carrier concentration changes over time. The first term on the right side of the formula represents the diffusion effect of carriers. The physical principle of diffusion can be understood as the natural migration of carriers from high-concentration areas to low-concentration areas driven by thermodynamics. n is the diffusion coefficient of the carrier, which determines the diffusion rate and reflects the diffusion capacity of the carriers in the material. It represents the second-order derivative of the concentration gradient, which describes the trend of concentration changes in space. The fundamental cause of the diffusion phenomenon is the existence of concentration gradient. When there is uneven concentration inside the material, the carriers tend to be evenly distributed through diffusion. For electronic products, the diffusion effect is usually the dominant factor when there is no significant electric field influence. It determines how the carriers are distributed in a balanced manner in the material. The second term It represents the carrier migration effect driven by electric field. nIt is the mobility of carriers, which reflects the speed at which carriers move under the action of a unit electric field. The influence of the electric field E(r, t) on carriers comes from the Coulomb force, that is, the electric field will generate a force in a specific area to push the charged carriers to move in a specific direction. The principle of this item can be understood from the classical law of motion of charges in an electric field: under the action of an electric field, positive charges and negative charges will move in opposite directions of the electric field, respectively, resulting in a redistribution of carrier concentration. In electronic products, the electric field effect is usually the dominant factor in the motion of carriers, especially under high voltage or high frequency conditions, the effect of the electric field on carriers is particularly significant. The last item G(r, t) is the carrier generation rate, which reflects the carrier generation process caused by external factors (such as photon excitation, electric field injection, etc.) at position r and time t. Its physical principle can be understood through the mechanism of photogenerated carriers or injected carriers in semiconductor materials. For example, in photovoltaic devices, photon energy can excite electrons in the material, thereby generating additional free electron and hole pairs in the conduction band, increasing the carrier concentration of the material. Similarly, an externally applied electric field can also change the concentration by injecting carriers. This term is crucial to describing the carrier changes in electronic products under dynamic working conditions, and it reveals how the external environment affects the carrier behavior inside the material by energy injection. Overall, the three terms of diffusion, electric field, and generation in the equation represent three different physical mechanisms, which work together to determine the changes in the carrier concentration distribution inside the target electronic product. In the absence of significant external electric field and carrier generation, the diffusion effect dominates, driving the carriers to migrate in the direction of uniform distribution. However, when there is an electric field, the electric field drive will induce the concentrated migration of carriers in the direction of the electric field, thereby changing the spatial distribution of the concentration. In addition, external factors (such as light, electric field, etc.) will dynamically increase or decrease the number of carriers through the generation term G(r, t). The interaction of these three mechanisms enables the equation to dynamically and accurately characterize the temporal and spatial variations of carrier concentration in target electronic products.

[0048] Example 4: Calculate the hot carrier energy spectrum of the target electronic product using the following formula:

[0049]

[0050] Where Φ(E, r, t) represents the density of hot carriers with energy E at position r and time t; N C is the effective state density, which represents the available state density of the conduction band in the semiconductor material; E represents the energy of the carrier; E F is the Fermi level, which represents the energy level benchmark in semiconductor materials; k Bis the Boltzmann constant; T is the temperature; q is the charge, which indicates the charge size of the carrier; λ is the mean free path, which indicates the average movement distance of the carrier between two scatterings; S is the carrier scattering rate.

[0051] Specifically, in the first part of the formula It reflects the occupation of carriers in the target electronic product relative to the effective state density of the conduction band at position r and time t. The effective state density N of the conduction band is a parameter that measures the number of quantum states that can be occupied by carriers in semiconductor materials. This ratio expresses the occupation ratio of carriers relative to available energy states at a specific position and time. The next part represents the statistical distribution of thermally excited carrier energy. According to the Fermi-Dirac distribution principle, the energy distribution of carriers in thermal equilibrium can be described by an exponential function of the difference between the energy and the Fermi level. Here E F represents the Fermi level, which is an energy benchmark in materials and determines the distribution state of electrons and holes in semiconductor materials. B is the Boltzmann constant, which is used to connect the relationship between energy and temperature. The temperature T represents the thermal state of the system. The exponential factor of this part It reflects the distribution of carriers in different energy states and reflects the transition behavior of carriers from low energy state to high energy state. The physical principle of this part can be understood as follows: at temperature T, thermal excitation enables some carriers to obtain enough energy to transition from a lower energy state to a higher energy state. In the next part of the formula In the above, the effect of electric field on hot carrier distribution is mainly described. Here, q represents the charge of the carrier, E(r, t) represents the electric field strength at position r and time t, and λ is the mean free path of the carrier, that is, the average distance the carrier moves between two scatterings. The exponential factor in this part can be regarded as an influencing factor of the electric field on the energy enhancement of the carrier. When the electric field acts on the carrier, an additional driving force will be generated to accelerate the carrier in the direction of the electric field, thereby increasing the energy state of the carrier. The effect of the electric field on the energy spectrum can be understood as follows: under the drive of the electric field, the energy distribution of the carrier will tend to a higher energy state, which is particularly significant under high field strength working conditions. Finally, S in the formula represents the scattering rate of the carrier, which reflects the probability of collision between the carrier and impurities, lattice defects, etc. during the movement. The scattering phenomenon is an important factor affecting the stability of carrier movement, because during the migration of the carrier, the scattering with other microstructures in the material will lead to energy loss and change the energy state of the carrier. The product term of the scattering rate S in the formula further corrects the calculation of the energy spectrum and reflects the regulatory effect of the scattering process on the distribution of hot carriers. This formula describes in detail the density of hot carriers with energy E at different positions r and time t through the integration of multiple factors. Its physical meaning is that the energy spectrum of hot carriers reflects the distribution of carriers inside electronic products under different energy states. By considering factors such as carrier concentration, Fermi level, temperature, electric field, scattering and mean free path, the formula can comprehensively and accurately characterize the thermal excitation behavior and electric field response of carriers in complex environments. This multi-factor joint modeling method is significantly innovative in the existing technology because it not only covers thermal effects, but also can dynamically reflect the influence of electric fields on carrier energy distribution.

[0052] Embodiment 5: Calculate the power consumption density by the following formula:

[0053] P local (r,t)=∫ 0 ∞ Φ(E,r,t)·E·SdE+|E(r,t)| 2 σ(n,T);

[0054] Among them, P local (r, t) is the power consumption density, which represents the power consumption caused by the movement of carriers in the material at position r and time t; σ(n, T) is the conductivity, which represents the conductivity of the material at carrier concentration n and temperature T.

[0055] Specifically, the left side of the formula P local(r, t) represents the power consumption density, which reflects the energy loss in the material due to the movement of carriers and thermal excitation at a specific position r and time t. The essence of power consumption density is to describe the loss of electrical energy or thermal energy, which is an important indicator for evaluating the performance and energy efficiency of electronic products. In electronic products, the size of power consumption directly affects its thermal management, energy utilization efficiency and long-term reliability. The first term of the formula ∫ 0 ∞ Φ(E,r,t)·E·S dE describes the power consumption due to the scattering effect of hot carriers. Here, Φ(E,r,t) represents the energy spectrum of hot carriers, which provides the density distribution of hot carriers at different energies E. The integral symbol ∫ 0 ∞ dE represents the sum of all energy states to cover all possible carrier energy states. Through this integration, the formula takes into account the contribution of the distribution of carriers at different energy levels to the power consumption. In this term, Φ(E,r,t)·E expresses the energy contribution carried by carriers in each energy state. Physically, this part represents the energy carried by each carrier with energy E when it moves in the material. Since hot carriers are caused by factors such as temperature and electric field, the movement of carriers in these energy states in the material will cause energy loss. In this part, S in the product term represents the scattering rate of the carrier. When carriers move in the material, they will scatter with the lattice, impurities or other carriers, resulting in energy loss. The scattering rate S reflects the probability or degree of this energy loss. The scattering term in the formula accurately describes the power consumption caused by the scattering effect by combining the hot carrier density and energy state. Therefore, the first term quantifies the power consumption density caused by scattering by comprehensive calculation of the hot carrier energy spectrum and the scattering rate. The second term of the formula

[0056] |E(r,t)| 2 σ(n,T) describes the ohmic loss due to the electric field. Here, |E(r,t)| 2It represents the square of the electric field strength and reflects the strength of the force exerted by the electric field on the carriers. In the material, the driving of the carriers by the electric field causes the carriers to accelerate, thus generating a current. As the current flows, a certain resistance is generated inside the material, causing energy to be dissipated in the form of heat. This phenomenon is called Ohmic loss. The conductivity σ(n,T) represents the conductivity of the material at the carrier concentration n and temperature T. The conductivity is closely related to the carrier concentration and temperature, and it reflects the conductivity of the material under the action of the electric field. Therefore, the second term of the formula combines the electric field and the conductivity to describe the Ohmic loss caused by the current inside the material. In principle, the formula describes the source of power consumption in detail in two parts. The first part focuses on the scattering effect of hot carriers in the material and quantifies the energy loss caused by the scattering of carriers at different energy states. The second part describes the Ohmic loss caused by the flow of current by combining the electric field and the conductivity. The two parts work together to form an overall description of the power consumption density. Compared with the traditional power consumption calculation method, the present invention achieves a more comprehensive characterization of power consumption by introducing the calculation of hot carrier energy spectrum and scattering rate. Traditional methods usually only focus on the effect of electric field on carriers, while ignoring the influence of thermal effect and scattering effect. However, in actual electronic products, especially under high temperature or high frequency conditions, the influence of scattering effect and thermal effect on power consumption cannot be ignored. Therefore, by considering these factors, the formula of the present invention can more accurately predict the power consumption density in the material and provide a scientific basis for energy efficiency optimization and thermal management of electronic products.

[0057] Embodiment 6: Calculate the reliability index of the target electronic product by the following formula:

[0058]

[0059] Among them, R(t) is the reliability index, which indicates the reliability of the target electronic product at time t. The closer R(t) is to 1, the higher the stability of the target electronic product is, and the closer it is to 0, the greater the probability of failure of the target electronic product is. τ is the time integral variable; P local (r, τ) represents the power consumption density at position r and time τ; P crit (T) is the critical power consumption density, which indicates the maximum power consumption density that the target electronic product can withstand at temperature T; n(r,τ) indicates the carrier concentration at position r and time τ; n max (T) is the maximum carrier concentration, which indicates the maximum carrier concentration that the target electronic product can withstand at temperature T;

[0060] Φ(E m ,r,τ) means at position r, time τ and energy E m The density of hot carriers under m represents the average energy; Φth (T) is the hot carrier threshold, which indicates the maximum hot carrier density that the target electronic product can withstand at temperature T; Ω represents the spatial area of ​​the entire target electronic product, which is integrated to obtain the global damage distribution.

[0061] Specifically, the left side of the formula R(t) represents the reliability of the electronic product at time t. This is a time-related indicator used to measure the performance change trend of the product during long-term operation. It takes the form of an exponential function, which is derived from the classical theory of electronic product reliability analysis. The evolution of reliability over time is often expressed in exponential form. This is because the failure probability of many electronic products tends to increase exponentially over time, while the reliability decays exponentially accordingly. This expression enables R(t) to accurately describe the stability of the target electronic product in long-term operation. The core of the right side of the formula lies in the integral part, which includes two layers: time integral and space integral. Time integral It reflects the cumulative impact on product reliability from the initial time to time t. Spatial integral ∫ Ω dΩ represents the sum of the spatial area of ​​the entire target electronic product, aiming to obtain the damage distribution inside the entire product. Through this double integration, the formula can fully reflect the comprehensive impact that electronic products suffer in time and space dimensions. In the integral part of the formula, the first parameter introduced is It represents the ratio of the local power consumption density to the critical power consumption density at position r and time τ. Here, P local (r, τ) is the power consumption density at position r and time τ, which reflects the local energy consumption caused by the movement of carriers under the action of the electric field. crit (T) is a temperature-related parameter that indicates the maximum power consumption density that the target electronic product can withstand. This ratio indicates whether the local power consumption is close to the critical value, that is, whether the product can operate stably at a specific temperature. The increase in power consumption will lead to an increase in the risk of thermal failure, so the size of this ratio directly affects the reliability of the product. Next, the second ratio that appears in the formula is represents the carrier concentration n(r, τ) at position r and time τ and the maximum carrier concentration n max (T). The carrier concentration directly reflects the electrical state inside the electronic product. If the carrier concentration is close to or exceeds the maximum allowable concentration, it may cause the electrical performance of the material to deteriorate, thereby increasing the risk of failure. Therefore, through this ratio, the formula can quantify the impact of changes in carrier concentration on product reliability. In addition, the third ratio in the formula It means that at position r and time τ, the energy is E m The hot carrier density Φ(E m , r, τ) and hot carrier threshold Φth Here, the hot carrier density Φ(E m ,r,τ) reflects the specific energy E m The carrier density under the threshold Φ th (T) represents the maximum hot carrier density that the material can withstand at temperature T. Hot carriers are formed due to high temperature or high electric field excitation, and their high density in the material may cause additional power consumption or thermal failure of the material. Therefore, the introduction of this ratio can measure the impact of thermal effects on the reliability of the material during operation.

[0062] Overall, the formula quantifies the combined impact of power consumption, carrier concentration and thermal effect on the reliability of the target electronic product by multiplying these three ratios. This multi-factor joint analysis method enables the system to more comprehensively evaluate the reliability of the product under actual working conditions, rather than being limited to the analysis of a single factor. Each ratio represents a potential failure mechanism: an increase in power density may lead to overheating, an increase in carrier concentration may lead to electrical failure, and an accumulation of hot carriers may lead to material damage. The combination of these three enables the formula to dynamically reflect the overall stability of the product in both spatial and temporal dimensions. In addition, the exponential form exp[-…] used in the formula represents the decay trend of reliability over time. The introduction of this form is derived from the classical theory in the reliability analysis of electronic products, that is, the cumulative effect of the failure rate over time will cause the reliability to decay exponentially. By combining the effects of power consumption, carrier concentration and hot carriers in an exponential form, the formula can better characterize the long-term stability of the target electronic product. Compared with the traditional reliability analysis method, the present invention achieves a more accurate description of the reliability index by introducing a comprehensive consideration of multiple factors. Traditional methods may only focus on a single factor of power consumption or temperature, while ignoring the complex interactions between electric fields, thermal effects, and carrier concentrations. In practical applications, the failure of electronic products is often the result of multiple factors working together. Therefore, by considering the ratio of power consumption density, carrier concentration, and hot carrier density, the formula of the present invention can more comprehensively and dynamically evaluate the reliability of products in complex working environments.

[0063] Embodiment 7: The multi-objective optimization equation of the target electronic product is expressed by the following formula:

[0064] min v,f {α 1 ∫ Ω P local (r,t)dΩ+α 2 max Ω [T]-α 3 R(t)};

[0065] Satisfy the constraints:

[0066]

[0067] Among them, V is voltage, f is frequency, both of which are control variables of the multi-objective optimization equation. By solving the multi-objective optimization equation, the optimal control voltage and optimal control frequency are obtained; α 1 , α 2 and α 3 are all preset weight parameters; ∫ Ω P local (r,t)dΩ represents the global power consumption of the entire target electronic product; max Ω [T] is the maximum temperature, which indicates the highest temperature inside the target electronic product; T max R is the maximum allowable temperature of the target electronic product, which is used to limit the temperature not exceeding the failure point of the material; min : Minimum reliability threshold.

[0068] Specifically, in this optimization equation, the first thing to understand is the power consumption part, which is expressed in the integral form ∫ Ω P local (r, t)dΩ. The physical meaning of this part is that it reflects the total power consumption of the target electronic product in the entire spatial region Ω. The power consumption is directly related to the movement of carriers in the material and the effect of the electric field. local By integrating (r, t), the system can quantify the cumulative effect of power consumption at different locations of the electronic product. This global power consumption calculation not only helps to understand the energy consumption of electronic products under high load conditions, but also provides accurate energy consumption data for optimizing control voltage and frequency. The second key factor to consider is the impact of temperature. The max in the optimization equation Ω The [T] term represents the maximum temperature inside the electronic product. This maximum temperature directly reflects the heat concentration inside the material. In high-frequency, high-power electronic products, local areas may generate high heat due to the presence of high carriers, causing the temperature to rise rapidly. The increase in temperature not only affects the mobility of the carriers, but may also cause thermal failure of the material, so the temperature must be strictly constrained in the optimization equation. In order to optimize product performance while controlling the temperature, the equation avoids the risk of local overheating by considering the maximum temperature. By properly adjusting the voltage V and frequency f, local heat accumulation can be reduced and the degradation of material performance due to overheating can be reduced. In the optimization equation, reliability R(t) is another important factor. The equation uses -α 3The reliability factor is considered in the form of R(t). The principle of this part is that reliability R(t) reflects the failure probability of electronic products at different times. Over time, if power consumption and temperature remain at high levels for a long time, the stability of the material will gradually weaken and the risk of failure will increase. Therefore, the negative sign -α introduced in the equation 3 R(t) indicates that the optimization goal is to maximize reliability and reduce the risk of failure. Through this design, the equation optimizes power consumption and temperature while not ignoring the stability requirements in long-term operation. During the optimization process, in order to ensure that the optimization results are reasonable under physical and material constraints, the equation also sets a series of constraints. First, the constraint ∫ Ω Φ(E,r,t)dE dΩ≤Φ th (T) limits the maximum value of hot carrier density. The upper limit of hot carrier density Φ th (T) reflects the maximum number of hot carriers that a material can withstand at a specific temperature. Too high a hot carrier density may cause thermal breakdown or degradation of the material. Therefore, the optimization equation must strictly control the accumulation of hot carriers to ensure the stability of the product.

[0069] In addition, the temperature constraint T≤T max The maximum allowable temperature T of the target electronic product at any location is clearly specified. max This constraint is set up to prevent the local temperature from exceeding the failure temperature of the material, thereby ensuring that the material will not be permanently damaged due to overheating. Through strict temperature control, problems such as material deformation and performance degradation caused by high temperature can be avoided, ensuring the safety of the product under different working conditions. Carrier concentration constraint n(r,t)≤n max (T) ensures that the carrier concentration inside the material does not exceed the maximum tolerance at a specific temperature. A high concentration of carriers may lead to an increase in the resistance of the material, an increase in power consumption, and even electrical breakdown. Therefore, by controlling the carrier concentration, the equation can further reduce the risk caused by electrical performance failure. Finally, the reliability constraint R(t)≥R min This ensures that the optimized reliability is always higher than the minimum threshold R min. This constraint can be regarded as the minimum requirement for the long-term stability of the system. In practical applications, electronic products must maintain sufficient stability in long-term operation to reduce the probability of failure. The electronic product performance prediction and optimization system successfully achieves a balance between power consumption, temperature and reliability through this multi-objective optimization equation. The design of the equation takes into account the various constraints of electronic products under different operating conditions, and adopts the optimal control voltage V and frequency f to reduce power consumption, control temperature and improve reliability. This multi-objective optimization method is significantly innovative because it not only solves the limitations of a single optimization objective, but also integrates multiple physical factors to make the optimization results more in line with actual application needs. Compared with traditional optimization methods, the multi-objective optimization equation of the present invention can more comprehensively reflect the performance changes of electronic products in complex working environments, thereby providing a scientific theoretical basis and precise data support for optimization control.

[0070] Example 8: α 1 The value range of α is 0.2 to 0.5; 2 The value range of α is 0.1 to 0.3; 3 The value range is 0.4 to 0.7; and it satisfies:

[0071] α 1 +α 2 +α 3 =1.

[0072] Specifically, these weight coefficients play a key role in optimization problems. They reflect the proportion of different objectives in the optimization process through linear combination. The value range of the weight coefficient is set according to the specific requirements of the system. By setting the upper and lower limits of each weight, the relative priority between different optimization objectives can be flexibly adjusted. First, α 1 The value range of α is between 0.2 and 0.5, which means that the importance of power consumption in the optimization process can be adjusted between 20% and 50% of the total weight. 1 When the value is large, the optimization goal will tend to reduce the global power consumption, thereby reducing energy consumption and heat loss. On the other hand, if the energy efficiency requirement in the system is not high, α can be set to 1 Setting α to a smaller value gives more weight to temperature or reliability optimization. 2 The value range of α is between 0.1 and 0.3. This range reflects the importance of temperature control in the optimization equation. Temperature control is essential to ensure material stability and avoid thermal failure. 2 A larger value means that the system is more tolerant to temperature changes, while a larger α 2 A value of α indicates that the maximum temperature needs to be more strictly controlled to ensure the safety of the system. 3The value range of α is between 0.4 and 0.7. The higher value range of this weight indicates that reliability has a higher priority in the entire optimization process. 3 A relatively small value indicates that the system has high reliability requirements and needs to ensure product stability and long-term performance during the optimization process. 3 A value of α indicates that more attention may be paid to improvements in power consumption or temperature in the optimization. It is worth noting that the sum of these weight coefficients must satisfy α 1 +α 2 +α 3 =1, this is to ensure the normalization of the optimization objectives, so that when all objectives work together in the optimization equation, the relative relationship of their weights remains unchanged. The introduction of this normalization condition ensures that in the optimization equation, no objective is ignored or overemphasized due to the setting of weights, thereby maintaining the balance of the overall optimization.

[0073] The preferred embodiments of the present disclosure are described above with reference to the accompanying drawings, but the scope of the present disclosure is not limited thereby. Any modification, equivalent substitution and improvement made by those skilled in the art without departing from the scope and essence of the present disclosure shall be within the scope of the present disclosure.

Claims

1. Electronic product performance prediction and optimization system, characterized in that: The system includes: a performance analysis part, a performance prediction part and a performance optimization control part; the performance analysis part is used to obtain product performance parameters of the target electronic product, calculate the carrier concentration distribution of the target electronic product by real-time acquisition of the electric field distribution of the target electronic product; calculate the hot carrier energy spectrum of the target electronic product based on the carrier concentration distribution; calculate the power consumption density based on the hot carrier energy spectrum of the target electronic product; the performance prediction part is used to calculate the reliability index of the target electronic product as a result of performance prediction based on the carrier concentration distribution, the hot carrier energy spectrum and the power consumption density; the performance optimization control part is used to construct a multi-objective optimization equation for the target electronic product based on the carrier concentration distribution, the hot carrier energy spectrum and the reliability index, and obtain the optimal control voltage and the optimal control frequency by solving the optimization equation.

2. The electronic product performance prediction and optimization system according to claim 1, characterized in that: The product performance parameters of the target electronic products include: carrier mobility, effective state density, Fermi level, carrier scattering rate, conductivity, maximum allowable temperature, maximum power consumption density, maximum carrier concentration and maximum hot carrier density.

3. The electronic product performance prediction and optimization system as claimed in claim 2, characterized in that: The carrier concentration distribution of the target electronic product is calculated using the following formula: Where n(r, t) is the carrier concentration distribution of the target electronic product at position r at time t; D n is the diffusion coefficient of carriers; μ n is the carrier mobility; E(r, t) is the electric field strength when the target electronic product is at position r at time t; G(r, t) is the carrier generation rate when the target electronic product is at position r at time t.

4. The electronic product performance prediction and optimization system as claimed in claim 3, characterized in that: The hot carrier energy spectrum of the target electronic product is calculated using the following formula: Where Φ(E, r, t) represents the density of hot carriers with energy E at position r and time t; N C is the effective state density, which represents the available state density of the conduction band in the semiconductor material; E represents the energy of the carrier; E F is the Fermi level, which represents the energy level benchmark in semiconductor materials; k B is the Boltzmann constant; T is the temperature; q is the charge, which indicates the charge size of the carrier; λ is the mean free path, which indicates the average movement distance of the carrier between two scatterings; S is the carrier scattering rate.

5. The electronic product performance prediction and optimization system according to claim 4, characterized in that: The power consumption density is calculated using the following formula: Among them, P local (r, t) is the power consumption density, which represents the power consumption caused by the movement of carriers in the material at position r and time t; σ(n, T) is the conductivity, which represents the conductivity of the material at carrier concentration n and temperature T.

6. The electronic product performance prediction and optimization system according to claim 5, characterized in that: The reliability index of the target electronic product is calculated using the following formula: Among them, R(t) is the reliability index, which indicates the reliability of the target electronic product at time t. The closer R(t) is to 1, the higher the stability of the target electronic product is, and the closer it is to 0, the greater the probability of failure of the target electronic product is. τ is the time integral variable; P local (r, τ) represents the power consumption density at position r and time τ; P crit (T) is the critical power consumption density, which indicates the maximum power consumption density that the target electronic product can withstand at temperature T; n(r, τ) indicates the carrier concentration at position r and time τ; n max (T) is the maximum carrier concentration, which indicates the maximum carrier concentration that the target electronic product can withstand at temperature T; Φ(E m , r, τ) represents the position r, time τ and energy E m The density of hot carriers under m represents the average energy; Φ th (T) is the hot carrier threshold, which indicates the maximum hot carrier density that the target electronic product can withstand at temperature T; Ω represents the spatial area of ​​the entire target electronic product, which is integrated to obtain the global damage distribution.

7. The electronic product performance prediction and optimization system according to claim 6, characterized in that: The multi-objective optimization equation of the target electronic product is expressed by the following formula: min V，f {α1∫ Ω P local (r,t)dΩ+α2max Ω [T]-α3R(t)}; Satisfy the constraints: Among them, V is voltage, f is frequency, both are control variables of the multi-objective optimization equation. By solving the multi-objective optimization equation, the optimal control voltage and optimal control frequency are obtained; α1, α2 and α3 are all preset weight parameters; ∫ Ω P local (r, t)dΩ represents the global power consumption of the entire target electronic product; max Ω [T] is the maximum temperature, which indicates the highest temperature inside the target electronic product; T max R is the maximum allowable temperature of the target electronic product, which is used to limit the temperature not exceeding the failure point of the material; min : Minimum reliability threshold.

8. The electronic product performance prediction and optimization system according to claim 7, characterized in that: The value range of α1 is 0.2 to 0.5; the value range of α2 is 0.1 to 0.3; the value range of α3 is 0.4 to 0.7; and they satisfy: α1+α2+α3＝1。

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