Electronic product performance prediction and optimization system

Abstract

The present invention discloses an electronic product performance prediction and optimization system, which relates to the field of data analysis and processing technology. 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 the product performance parameters of the target electronic product, and calculate the power consumption density by real-time acquisition of the electric field distribution of the target electronic product; the performance prediction part is used to use the carrier concentration distribution, hot carrier energy spectrum and power consumption density as the result of performance prediction; 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, hot carrier energy spectrum and reliability index, and obtain the optimal control voltage and optimal control frequency by solving the optimization equation. The present invention realizes the accurate prediction of the performance of electronic products, and combines the multi-factor optimization strategy to dynamically adjust the control voltage and frequency to achieve all-round optimization of product performance.

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 typically employs single-objective optimization methods, such as power consumption optimization, thermal control, or reliability improvement. These optimization techniques are designed to address specific performance objectives, and common approaches include low-power design, electric field or current control, thermal management techniques, and reliability prediction models. For example, power optimization techniques often directly reduce power density by lowering voltage or current, but this can lead to performance degradation or slower response speeds in electronic products. Thermal control techniques, on the other hand, typically employ methods such as heat conduction materials, heat sinks, or fans to mitigate localized overheating. However, these thermal management methods often simply control temperature and fail to optimize the generation and distribution of hot carrier energy from the perspective of electric field distribution and carrier behavior.

[0003] The biggest flaw of existing optimization techniques, focusing on a single objective, is their failure to fully consider the complex interrelationships between various performance factors. For example, while reducing power consumption, this can negatively impact the overall reliability of an electronic product. When implementing thermal management, excessively limiting temperature increases can increase material resistance, leading to increased power consumption. Furthermore, existing technologies often lack comprehensive multi-objective optimization methods, failing to strike a reasonable balance between power consumption, temperature, and reliability. Failures in modern electronic products are often the result of the combined effects of multiple factors. Therefore, ignoring the interrelationships between these factors can significantly reduce optimization effectiveness.

[0004] While existing technologies have achieved some success in single-objective performance optimization, they still face several major challenges: Limitations of multi-objective optimization methods: Most existing optimization techniques are based on a single objective, such as power consumption optimization, thermal control, or reliability improvement. However, the design and optimization of electronic products involve multiple interrelated performance metrics, such as power consumption, temperature, and reliability. These performance metrics often have mutually constrained relationships, and when optimizing one objective, the impact on other objectives can be easily overlooked. For example, simply reducing power consumption can slow carrier movement, thereby reducing overall performance; while excessively increasing power density control can increase thermal effects, further impacting material reliability. Lack of accurate modeling of dynamic changes: Existing optimization methods often rely on static models or simple single-factor models, failing to fully account for the dynamic changes in electronic products under complex operating conditions. For example, under dynamic operating conditions, changes in electric field strength, the generation and scattering of hot carriers, and real-time variations in carrier concentration can significantly impact the overall performance of the product. These dynamic changes are often difficult for existing models to accurately capture, resulting in limited prediction and optimization effectiveness of existing technologies. Summary of the Invention

[0005] The present disclosure provides an electronic product performance prediction and optimization system, which achieves more accurate prediction of the performance of electronic products and combines multi-factor optimization strategies to dynamically adjust control voltage and frequency to achieve all-round optimization of 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 section, a performance prediction section, and a performance optimization control section; the performance analysis section 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 section is used to calculate the reliability index of the target electronic product as a result of performance prediction based on the carrier concentration distribution, hot carrier energy spectrum, and power consumption density; the performance optimization control section is used to construct a multi-objective optimization equation for the target electronic product based on the carrier concentration distribution, hot carrier energy spectrum, and reliability index, and obtain the optimal control voltage and optimal control frequency by solving the optimization equation.

[0008] Furthermore, 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.

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

[0010]

[0011] Where n(r, t) is the carrier concentration distribution of the target electronic product at time t when the target electronic product is at position r; D n is the diffusion coefficient of carriers; μ n is the carrier mobility; E(r, t) is the electric field intensity 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 using 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 using 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 electrical conductivity, which represents the electrical conductivity of the material at carrier concentration n and temperature T.

[0018] Furthermore, the reliability index of the target electronic product is calculated using 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. 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) represents 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) 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 represents 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 {α1∫ Ω P local (r,t)dΩ+α2max Ω [T]-α3R(t)};

[0024] Satisfy the constraints:

[0025]

[0026] 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, indicating the highest temperature inside the target electronic product; T max is the maximum allowable temperature of the target electronic product, which is used to limit the temperature not to exceed the failure point of the material; R min : Minimum reliability threshold.

[0027] Furthermore, 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:

[0028] α1+α2+α3=1.

[0029] The electronic product performance prediction and optimization system of the present invention has the following beneficial effects: By constructing a multi-objective optimization equation, the present invention achieves comprehensive optimization of electronic product performance. This optimization equation not only minimizes global power consumption but also simultaneously controls the maximum temperature within the product within a safe range and assesses the product's long-term stability by incorporating reliability indicators. Unlike the single optimization objective methods commonly used in the prior art, the optimization method of the present invention is able to find a reasonable balance between power consumption, temperature, and reliability. Through this comprehensive optimization approach, the system reduces power consumption while effectively controlling temperature rise and ensuring product reliability. As a result, electronic products exhibit higher stability and energy efficiency during long-term operation, significantly reducing the risk of malfunction and thermal failure. The present invention utilizes dynamic modeling technology to track the carrier concentration distribution, electric field distribution, and hot carrier energy spectrum within electronic products in real time. The core of this dynamic modeling technology lies in its ability to accurately describe the motion of carriers in materials and changes in their energy states through mathematical tools such as partial differential equations and probability distributions. By monitoring these dynamic factors in real time, the system can promptly adjust the optimization strategy to ensure that voltage and frequency remain within the optimal range under different operating conditions. Compared with traditional static modeling methods, the dynamic modeling technology of the present invention can better cope with the performance fluctuations of electronic products under complex working conditions, ensuring 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 by 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 more clear and understandable, the present disclosure is further described in detail below with reference to 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 intended to limit the present disclosure.

[0032] Example 1, reference Figure 1: An electronic product performance prediction and optimization system, 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 the product performance parameters of the 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, hot carrier energy spectrum and 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, hot carrier energy spectrum and reliability index, and obtain the optimal control voltage and optimal control frequency by solving the optimization equation.

[0033] Specifically, the foundational work of the performance analysis component is the real-time acquisition of the electric field distribution of the target electronic product. This acquisition is the first step in the system's development, aiming to understand the internal electric field variations of the electronic product. The electric field distribution within an electronic product is affected by a variety of factors, such as external voltage, the conductivity of the product's internal materials, and its geometric structure. Because the electric field directly drives the movement of electrons and holes, changes in the electric field distribution directly impact the flow and concentration distribution of carriers. Using sensors and signal acquisition equipment, the system acquires real-time electric field data within the electronic product. To more accurately characterize the electric field distribution, the system may employ multi-point or multi-dimensional acquisition methods to obtain higher-resolution electric field information. This information not only serves as the foundation for performance analysis but also provides essential input for subsequent carrier concentration calculations. Based on this acquired electric field data, the system further calculates the carrier concentration distribution within the target electronic product. The carrier concentration distribution determines the current transfer characteristics within the electronic product and is a key parameter reflecting its performance. The basic principle is that under the action of an electric field, carriers (electrons and holes) will migrate in semiconductor materials 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 material parameters, and differential equations may be used to characterize the effect of the electric field on carrier motion. 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 a hot carrier energy spectrum for the target electronic product. The so-called hot carrier energy spectrum refers to the distribution of energy states caused by the thermal motion of carriers within the electronic product. For high-performance electronic products, the influence of thermal effects on carrier motion cannot be ignored. Under the influence of an applied electric field, carriers not only migrate spatially but also acquire 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 to describe the distribution of carriers at specific energy states through a comprehensive analysis of the carrier concentration and temperature field. This analysis process may involve solving the thermal equilibrium state of carriers and statistically modeling the probability density of carriers at different energy states. The hot carrier energy spectrum not only reflects the activity of carrier motion in the material but also provides important reference information for subsequent power consumption analysis. Based on the obtained hot carrier energy spectrum, the system further calculates the power consumption density of the target electronic product. Power consumption density is a key metric for measuring the energy consumption of electronic products during operation. It reflects the product's energy efficiency and internal thermal management. The system derives the power consumption density distribution by accurately calculating the energy states of hot carriers. The basic principle is that carrier movement speed and collision frequency vary under different energy states, and these changes lead to different power consumption. Therefore, the calculation of power consumption density generally requires considering the energy losses of carriers at different energy states and the relationship between these losses and the electric field strength and material conductivity. The power consumption density calculation formula is essentially a manifestation of the law of conservation of energy. By accurately modeling energy flow, the system can identify high-energy consumption areas in electronic products under different operating conditions. The power consumption density calculation results 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 component comprehensively analyzes multi-dimensional physical quantities to reveal the performance variations of electronic products under different operating conditions. Compared to existing technologies, this system is unique in that it not only focuses on single electric field or temperature distributions but also comprehensively characterizes electronic product performance through the combined analysis of multiple parameters, including carrier concentration, hot carrier energy spectrum, and power consumption density. Existing technologies typically analyze only a single performance parameter, but this system, through the comprehensive calculation of multiple parameters, can more accurately predict the operating state and performance variations of electronic products in complex environments. This multi-dimensional performance analysis approach provides an innovative solution for the refined management and optimization of electronic products. The performance analysis component of the electronic product performance prediction and optimization system precisely collects the electric field distribution of the target electronic product to construct a multi-dimensional model reflecting the carrier concentration, hot carrier energy state, and power consumption density. The electric field distribution is the basis for the carrier concentration distribution, and changes in carrier concentration directly affect the construction of the hot carrier energy spectrum. Ultimately, the calculation of the hot carrier energy spectrum provides critical data support for power consumption density analysis. This interconnected analysis process not only reveals the complex electrical and thermal behavior within electronic products but also lays a solid foundation for subsequent performance prediction and optimized control. These innovative performance analysis techniques, by introducing multi-dimensional physical parameters, overcome the limitations of single-parameter analysis in existing technologies, enabling the system to more comprehensively and accurately evaluate electronic product performance.

[0036] Carrier concentration is a fundamental physical quantity that describes the dynamic distribution of electrons and holes in semiconductor materials. The number and distribution of carriers directly influences the material's electrical conductivity and energy transfer properties, making it a core performance metric for electronic products. In predictive models, carrier concentration distribution not only serves as a crucial indicator of the current operating state of an electronic product but also provides essential input data for systematic analysis of energy changes during carrier migration. By modeling carrier concentration at different locations, the system can capture the flow characteristics of carriers at different energy states, thereby more accurately describing the electric field and current changes within the electronic product.

[0037] Secondly, the performance prediction component further analyzes the carrier energy state distribution using the hot carrier energy spectrum. The hot carrier energy spectrum reflects the distribution of carriers between different energy states under the influence of thermal motion. For electronic products, the presence of hot carriers has a significant impact on the performance and reliability of the product. In particular, in high-temperature or high-frequency environments, thermal effects can lead to enhanced carrier migration, which in turn causes energy loss in the material and localized temperature rise. By modeling the hot carrier energy spectrum, the system can fully understand the carrier energy state distribution 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 characteristics of carrier motion in complex environments, providing more accurate data support for reliability prediction. Furthermore, the performance prediction component also uses power consumption density as a key input parameter. Power consumption density reflects the energy consumption of electronic products under different operating conditions and is an important indicator for measuring the product's energy efficiency and thermal management effectiveness. Changes in power consumption directly affect the operating temperature of electronic products, and rising temperatures in turn affect carrier migration and thermal excitation processes. Therefore, power consumption density is not only a measure of product performance but also a key 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 derives a comprehensive reliability index by analyzing the interaction between various factors. In the process of constructing 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 in 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 component first uses the reliability metrics derived from the performance prediction component as input and combines them with the carrier concentration distribution and hot carrier energy spectrum obtained in the previous analysis. Reliability metrics are more than just a single metric; they directly reflect the failure risk and performance variations of electronic products under different operating conditions. Therefore, reliability metrics are considered a key reference parameter when constructing the optimization model. Simultaneously, the carrier concentration distribution and hot carrier energy spectrum provide detailed physical information about the internal state of the electronic product. This information encompasses the electrical and thermal characteristics exhibited by the electronic product during operation, providing comprehensive input data for multi-objective optimization. To achieve performance optimization, the system constructs a multi-objective optimization model based on this input data. The core concept of this optimization model is to mathematically express multiple performance objectives for the electronic product and then solve them using an optimization algorithm to find the optimal control solution. In this process, the multi-objective optimization equation comprehensively considers control voltage, control frequency, and related reliability and power consumption constraints. Control voltage and control frequency, as key control parameters of electronic products, directly affect carrier migration speed, 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] When solving the optimization equations, the system typically employs an advanced optimization algorithm, such as a genetic algorithm or a particle swarm optimization algorithm. These algorithms perform a global search within a multi-dimensional parameter space to find the optimal control solution. This global search approach allows the system to select the optimal solution from a large number of candidate solutions, avoiding the local optimum often encountered in traditional optimization methods. Furthermore, the performance optimization control component specifically considers the dynamic characteristics of electronic products under varying operating conditions. By incorporating a dynamic feedback mechanism, the system monitors performance changes of electronic products in real time during actual applications and adjusts the weights and constraints in the optimization model accordingly. This dynamic feedback mechanism enables the system to maintain high adaptability and stability in complex operating environments, further improving the accuracy of optimization control. Notably, the performance optimization control component not only focuses on overall product performance but also specifically considers the balance between energy efficiency and reliability. In many high-performance electronic products, the pursuit of higher computing speeds or enhanced functionality often comes with increased energy consumption and increased reliability risks. Therefore, in constructing the optimization model, the system employs a multi-objective trade-off strategy, comprehensively optimizing energy efficiency, reliability, and performance improvements. This strategy enables the system to achieve an 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] Example 2: The product performance parameters of the target electronic product 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.

[0041] Specifically, carrier mobility, a parameter that describes the motion characteristics of electrons and holes in a material, directly reflects the carrier response speed under the action of an external electric field. The higher the mobility, the greater the carrier mobility in the material, thus affecting the material's conductivity. In optimization control, carrier mobility serves as a bridge between the electric field distribution and carrier behavior, determining the efficiency of carrier movement and the overall conductivity of the material. By dynamically analyzing mobility, the system can accurately assess changes in the conductivity of electronic products under different operating conditions, providing a strong basis for optimization control. The effective density of states refers to the number of effective quantum states of carriers in a semiconductor material and is determined by the material's energy band structure. The effective density of states reflects the number of energy levels available for carriers to occupy 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 density of states, the system can further deduce the carrier distribution, providing accurate data support for subsequent energy spectrum analysis.

[0042] The Fermi level is a key parameter describing the carrier energy state. It reflects the distribution of electrons and holes in a material under thermal equilibrium. Changes in the Fermi level directly affect the material's electrical properties, making its precise setting particularly important in performance prediction. By dynamically adjusting the Fermi level, the system can flexibly adapt to varying operating environments and conditions, thereby improving the accuracy of the prediction model. The carrier scattering rate describes the probability of carriers being scattered by defects or impurities as they move through a material. The scattering process affects carrier mobility and energy loss, and therefore directly impacts the performance and power consumption of electronic products. In optimization control, the system can reduce carrier energy loss by adjusting the scattering rate, thereby improving the energy efficiency of electronic products.

[0043] Conductivity, a parameter reflecting the conductive properties of a material, directly determines the current transmission capacity of electronic products. Conductivity is closely related to carrier concentration and mobility, making its precise setting crucial for performance prediction and optimization control. By dynamically adjusting conductivity, the system can effectively control the current distribution and energy efficiency of electronic products. The maximum allowable temperature refers to the highest temperature an electronic product can withstand during operation. High temperatures often lead to enhanced carrier excitation and may cause thermal failure of the material. Therefore, in performance prediction and optimization, the system must monitor the operating temperature of the electronic product in real time to ensure it does not exceed the maximum allowable temperature to avoid performance degradation and failure caused by overheating. The maximum power consumption density reflects the maximum energy consumption of an electronic product under specific conditions. This parameter directly affects the thermal management and energy efficiency of the electronic product, making it a key constraint to consider in optimization control. By strictly controlling the maximum power consumption density, the system can improve the energy efficiency of electronic products and reduce the risk of thermal failure while maintaining performance. The maximum carrier concentration and the maximum hot carrier density are important parameters that describe the carrier and thermal excitation states in a material. Their settings directly affect the current transmission characteristics and thermal excitation effects of electronic products. In optimization control, the system can effectively adjust the operating state of electronic products by real-time monitoring of these two parameters, ensuring that they always operate in an efficient and stable range.

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

[0045]

[0046] Where n(r, t) is the carrier concentration distribution of the target electronic product at time t when the target electronic product is at position r; D n is the diffusion coefficient of carriers; μ n is the carrier mobility; E(r, t) is the electric field intensity 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 change 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 the 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 the diffusion phenomenon 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 ability of the carrier in the material. It represents the second-order derivative of the concentration gradient, which describes the trend of concentration change in space. The fundamental driving force 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. Here μ nis the carrier mobility, which reflects the speed at which carriers move under a unit electric field. The influence of the electric field E(r, t) on carriers stems from the Coulomb force, which generates a force within a specific region that propels charged carriers in a specific direction. The principle behind this term can be understood from the classical law of charge motion in an electric field: under the influence of an electric field, positive and negative charges move in opposite directions, respectively, resulting in a redistribution of carrier concentration. In electronic products, the electric field effect is often the dominant factor in carrier motion, especially under high voltage or high frequency conditions, where the effect of the electric field on carriers is particularly significant. The last term, G(r, t), is the carrier generation rate, which reflects the generation of carriers at position r and time t due to external factors (such as photon excitation or electric field injection). Its physical principle can be understood by understanding the mechanisms of photogenerated or injected carriers in semiconductor materials. For example, in photovoltaic devices, photon energy can excite electrons in the material, generating additional free electron-hole pairs in the conduction band and increasing the material's carrier concentration. Similarly, an externally applied electric field can also modify the concentration by injecting carriers. This term is crucial for describing carrier variations in electronic devices under dynamic operating conditions, revealing how the external environment influences carrier behavior within the material through energy injection. Overall, the three terms in this equation—diffusion, electric field, and generation—represent three distinct physical mechanisms that, together, determine the carrier concentration distribution within the target electronic device. In the absence of a significant external electric field and carrier generation, diffusion dominates, driving carrier migration toward a uniform distribution. However, when an electric field is applied, the field-driven effect induces concentrated carrier migration in the direction of the field, thereby altering the spatial distribution of the concentration. Furthermore, external factors (such as light and electric fields) can 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 density of states of the conduction band at position r and time t. The effective density of states N of the conduction band is a parameter that measures the number of quantum states that can be occupied by carriers in a semiconductor material. This ratio expresses the proportion of carrier occupation relative to the available energy states at a specific position and time. The following 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 their energy and the Fermi level. Here E F represents the Fermi level, which is an energy benchmark in the material and determines the distribution state of electrons and holes in the semiconductor material. B is the Boltzmann constant, which is used to connect the relationship between energy and temperature. 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 lower energy state to higher energy state. In the next part of the formula The equation ( ) mainly describes the effect of the electric field on hot carrier distribution. Here, q represents the carrier charge, E(r, t) represents the electric field strength at position r and time t, and λ is the carrier mean free path, or the average distance a carrier travels between two scattering events. The exponential factor in this section can be considered a factor influencing the electric field's effect on carrier energy. When an electric field acts on carriers, it generates an additional driving force, accelerating them in the direction of the field, thereby increasing their energy state. The effect of the electric field on the energy spectrum can be understood as: driven by the electric field, the carrier energy distribution shifts toward higher energy states, which is particularly pronounced under high field strength operating conditions. Finally, S in the formula represents the carrier scattering rate, which reflects the probability of collisions between carriers and impurities, lattice defects, and other objects during their motion. Scattering is a crucial factor affecting the stability of carrier motion. During carrier migration, scattering from other microstructures in the material results in energy loss and changes in the carrier energy state. 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 times t through the integration of multiple factors. Its physical significance is that the energy spectrum of hot carriers reflects the distribution of carriers inside electronic products at 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 the electric field on the carrier energy distribution.

[0052] Example 5: Calculate the power consumption density using 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 electrical 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 carrier movement and thermal excitation at a specific location r and time t. The power consumption density essentially describes the loss of electrical or thermal energy, which is an important indicator for evaluating the performance and energy efficiency of electronic products. In electronic products, the amount of power consumption directly affects their 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 dissipation 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 carriers at different energies E. The integral symbol ∫0 ∞ dE represents the summation 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 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 moving 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 result in energy loss. In this part, S in the product term represents the scattering rate of carriers. 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 through a 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)| 2σ(n, T) represents the square of the electric field strength and reflects the strength of the force exerted by the electric field on charge carriers. In a material, the electric field's drive on charge carriers causes them to accelerate, generating a current. As current flows, a certain resistance is generated within the material, causing energy to be dissipated as heat. This phenomenon is known as ohmic losses. The conductivity σ(n, T) represents the material's ability to conduct electricity at carrier concentration n and temperature T. Conductivity is closely related to carrier concentration and temperature, reflecting the material's ability to conduct electricity under the influence of an electric field. Therefore, the second term in the equation combines the electric field and conductivity to describe the ohmic losses caused by current flow within the material. In principle, this equation describes the sources of power dissipation in detail in two parts. The first part focuses on the scattering effect of hot carriers in the material, quantifying the energy loss caused by scattering of carriers at different energy states. The second part describes the ohmic losses caused by current flow by combining the electric field and conductivity. These two components work together to form an overall description of power dissipation density. Compared with traditional power consumption calculation methods, 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 the electric field on carriers, while ignoring the influence of thermal effects and scattering effects. However, in actual electronic products, especially under high temperature or high frequency conditions, the impact of scattering effects and thermal effects on power consumption cannot be ignored. Therefore, by taking these factors into account, 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] Example 6: Calculate the reliability index of the target electronic product using 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. 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) represents 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) represents the 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 represents 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, which 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 shows exponential decay 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 within the entire product. Through this double integration, the formula can fully reflect the comprehensive impact that the electronic product suffers in the 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. Increased power consumption will lead to an increased 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 The carrier concentration n(r, τ) at position r and time τ is related to the maximum carrier concentration n max The carrier concentration directly reflects the electrical state inside the electronic product. If the carrier concentration approaches 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 Indicates 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 (T). 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 a material can withstand at temperature T. Hot carriers are formed by excitation at high temperatures or high electric fields, and their high density in a material can lead to excessive power consumption or thermal failure. Therefore, the introduction of this ratio can measure the impact of thermal effects on material reliability during operation.

[0062] Overall, the formula quantifies the combined impact of power consumption, carrier concentration, and thermal effects on the reliability of the target electronic product by multiplying these three ratios. This multi-factor combined analysis approach enables a more comprehensive assessment of the product's reliability under actual operating conditions, rather than simply analyzing a single factor. Each ratio represents a potential failure mechanism: increased power density can lead to overheating, increased carrier concentration can lead to electrical failure, and the accumulation of hot carriers can cause material damage. The combination of these three factors enables the formula to dynamically reflect the overall stability of the product across both spatial and temporal dimensions. Furthermore, the exponential form exp[-…] used in the formula represents the reliability decay trend over time. This form is based on the classic theory in electronic product reliability analysis that the cumulative effect of failure rate over time leads to exponential reliability decay. By exponentially combining the effects of power consumption, carrier concentration, and hot carriers, the formula can better characterize the long-term stability of the target electronic product. Compared to traditional reliability analysis methods, this invention achieves a more precise description of reliability indicators by incorporating multiple factors into the comprehensive consideration. Traditional methods may focus solely on power consumption or temperature, ignoring the complex interactions between electric fields, thermal effects, and carrier concentration. In practical applications, however, electronic product failures are often the result of the combined effects of multiple factors. Therefore, by considering the ratio of power consumption density, carrier concentration, and hot carrier density, the formula proposed in this paper can more comprehensively and dynamically assess product reliability in complex operating environments.

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

[0064] min v,f {α1∫ Ω P local (r,t)dΩ+α2max Ω [T]-α3R(t)};

[0065] Satisfy the constraints:

[0066]

[0067] 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, indicating the highest temperature inside the target electronic product; T max is the maximum allowable temperature of the target electronic product, which is used to limit the temperature not to exceed the failure point of the material; R 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. By calculating the power consumption density P in the entire spatial region 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 ΩThe term [T] represents the maximum temperature inside the electronic product. This maximum temperature directly reflects the heat concentration within the material. In high-frequency, high-power electronic products, localized regions may generate high heat due to the presence of high carriers, leading to rapid temperature increases. This temperature increase not only affects carrier mobility but can also cause thermal failure of the material. Therefore, strict temperature constraints must be placed in the optimization equation. To optimize product performance while controlling temperature, the equation considers the maximum temperature to avoid the risk of local overheating. By appropriately adjusting the voltage V and frequency f, local heat accumulation can be reduced, minimizing material degradation due to overheating. Reliability R(t) is another important factor in the optimization equation. The equation incorporates this reliability factor in the form of -α3R(t). The principle behind this is that reliability R(t) reflects the probability of failure of an electronic product at different times. Over time, if power consumption and temperature remain high for a long time, the material's stability will gradually weaken and the risk of failure will increase. Therefore, the negative sign -α3R(t) introduced in the equation indicates that the optimization goal is to maximize reliability and minimize failure risk. Through this design, the equation optimizes power consumption and temperature while not neglecting 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 a material can withstand at a specific temperature. Excessive hot carrier density can cause thermal breakdown or degradation of the material. Therefore, the optimization equation must strictly control the accumulation of hot carriers to ensure product stability.

[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 established 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. By strictly controlling the temperature, 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. The 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 minThis 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 achieved 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 makes the optimization results more in line with actual application needs by integrating multiple physical factors. 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: 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 the following conditions are satisfied:

[0071] α1+α2+α3=1.

[0072] Specifically, these weight coefficients play a key role in the optimization problem. Through linear combination, they reflect the weight of different objectives in the optimization process. The range of weight coefficients is determined based on the specific requirements of the system. By setting upper and lower limits for each weight, the relative priority of different optimization objectives can be flexibly adjusted. First, the value of α1 ranges from 0.2 to 0.5, meaning that the importance of power consumption in the optimization process can be adjusted between 20% and 50% of the total weight. When α1 is set to a larger value, the optimization objective will favor reducing global power consumption, thereby reducing energy consumption and heat loss. On the other hand, if energy efficiency is not a high requirement in the system, α1 can be set to a smaller value, allocating more weight to temperature or reliability optimization. Second, the value of α2 ranges from 0.1 to 0.3. This design reflects the importance of temperature control in the optimization equation. Temperature control is crucial for ensuring material stability and avoiding thermal failure. A smaller α2 value means that the system is more tolerant of temperature fluctuations, while a larger α2 value indicates that stricter control of the maximum temperature is required to ensure system safety. Finally, the value range of α3 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. A larger α3 value indicates that the system has higher requirements for reliability and needs to ensure the stability and long-term performance of the product during the optimization process. A relatively small α3 value indicates that more attention may be paid to improvements in power consumption or temperature during the optimization. It is worth noting that the sum of these weight coefficients must satisfy α1+α2+α3=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 will be ignored or overemphasized due to the setting of the weight, 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 are not intended to limit the scope of the present disclosure. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present disclosure shall fall within the scope of the present disclosure.

Claims

1. Electronic product performance prediction and optimization system, characterized by: 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, hot carrier energy spectrum and 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, hot carrier energy spectrum and reliability index, and obtain the optimal control voltage and optimal control frequency by solving the optimization equation; Calculate the reliability index of the target electronic product using the following formula: ； in, Reliability index, which indicates the target electronic product’s reliability over time. reliability when The closer it 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. is the time-integrated variable; Indicates the location and time Power consumption density under is the critical power dissipation density, which indicates the The maximum power consumption density that the target electronic product can withstand; Indicates the location and time The carrier concentration under is the maximum carrier concentration, indicating that the The maximum carrier concentration that the target electronic product can withstand; Indicates the location ,time and energy The density of hot carriers under represents the average energy; is the hot carrier threshold, which indicates the temperature The maximum hot carrier density that the target electronic product can withstand; represents the spatial region of the entire target electronic product, which is integrated to obtain the global damage distribution; The multi-objective optimization equation of the target electronic product is expressed as follows: ； Satisfy the constraints: ； in, is the voltage, is the 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; , and All are preset weight parameters; Represents the global power consumption of the entire target electronic product; is the maximum temperature, indicating the highest temperature inside the target electronic product; The maximum allowable temperature of the target electronic product, used to limit the temperature to not exceed the failure point of the material; : Minimum reliability threshold.

2. The electronic product performance prediction and optimization system according to claim 1, wherein: 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 according to claim 2, wherein: The carrier concentration distribution of the target electronic product is calculated using the following formula: ； in, For target electronic products at location When, in time The carrier concentration distribution when ; is the diffusion coefficient of carriers; is the carrier mobility; For target electronic products at location When, in time The electric field strength at For target electronic products at location When, in time The carrier generation rate at .

4. The electronic product performance prediction and optimization system according to claim 3, wherein: The hot carrier energy spectrum of the target electronic product is calculated using the following formula: ； in, Indicates the location ,time The energy is The density of hot carriers; is the effective density of states, which represents the available state density of the conduction band in the semiconductor material; represents the energy of the carrier; is the Fermi level, which represents the energy level benchmark in semiconductor materials; is the Boltzmann constant; is temperature; is the charge amount, which indicates the charge size of the carrier; is the mean free path, which represents the average distance that a carrier moves between two scatterings; is the carrier scattering rate.

5. The electronic product performance prediction and optimization system according to claim 4, wherein: The power consumption density is calculated using the following formula: ； in, is the power consumption density, indicating the location and time The power consumption caused by the movement of carriers in the lower material; Is the conductivity, which indicates the carrier concentration of the material and temperature The electrical conductivity of the lower.

6. The electronic product performance prediction and optimization system according to claim 5, wherein: The value range of is 0.2 to 0.5; The value range of is 0.1 to 0.3; The value range is 0.4 to 0.7; and it satisfies: 。

Images