CN116484686A - Two-stage TSV intelligent thermal cooperative optimization method - Google Patents
Two-stage TSV intelligent thermal cooperative optimization method Download PDFInfo
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Abstract
The application relates to the field of integrated circuits, and particularly provides a two-stage TSV intelligent thermal cooperative optimization method, which comprises the following steps of: s1, constructing a model and determining the optimal grid size; s2, coarse grid low-precision rapid optimization; s3, fine grid high-precision accurate optimization; s4, outputting and verifying optimal parameters. The invention provides a two-stage TSV intelligent thermal cooperative optimization method. Compared with the traditional method, the method reduces the time for acquiring the data set, and then increases the data quantity in the pre-optimization area, so that the final optimization result is more accurate. Specifically, the first stage is to search the TSV peak temperature coarse grid quickly with low precision, and the second stage is to search the TSV peak temperature fine grid accurately with high precision.
Description
Technical Field
The application relates to the field of integrated circuits, in particular to a two-stage TSV intelligent thermal cooperative optimization method.
Background
Along with the increasing scale of system integrated chips, the three-dimensional integration technology can effectively reduce the area of a microsystem product in the horizontal direction, simultaneously reduce the length of interconnection lines and reduce signal delay, so that the system has the advantages of small size, high performance and low power consumption. As power consumption density increases, thermal problems in integrated circuits are becoming more and more important. In 3D ICs, heat accumulation problems within minute volumes can cause degradation and even failure of system performance. Through Silicon Vias (TSVs) are critical components in three-dimensional integrated circuits, whose performance determines the performance of the three-dimensional integrated circuit. Therefore, it is important to explore the peak temperature of the TSV.
The problem of thermal optimization based on the combination of the artificial neural network and the particle swarm optimization algorithm can be solved well, the problems that the traditional design method depends on expert experience and has low design efficiency are solved, however, the accuracy of the neural network is ensured to obtain enough data, and time-consuming finite element simulation is still needed to obtain the data. The existing scheme is an intelligent thermal modeling technology based on a neural network auxiliary optimization algorithm, the method comprises the steps of firstly sampling in a design space to obtain combinations among design parameters, then obtaining a TSV peak temperature database of all the design parameter combinations by using finite element simulation software, then training a neural network by using the obtained database, constructing a mapping relation between the design parameters and performance parameters, then establishing a TSV peak temperature evaluation criterion, optimizing the peak temperature by using a population optimization algorithm based on the established neural network and combining the TSV peak temperature evaluation criterion, and finally obtaining the optimal design parameters and performance parameters. However, in order to ensure the accuracy of the neural network, a large number of time-consuming finite element simulations are required, and the generated design parameter combinations are uniform throughout the design space, which results in less data around the optimal region and low optimization accuracy.
In summary, the existing optimization method needs longer time and has lower optimization efficiency.
Disclosure of Invention
The invention aims to provide a two-stage TSV intelligent thermal cooperative optimization method aiming at the defects in the prior art, so as to solve the problems that the conventional optimization method needs longer time, has lower optimization efficiency and takes time to acquire training data.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the application provides a two-stage TSV intelligent thermal cooperative optimization method, which comprises the following steps: s1, constructing a model and determining the optimal grid size; s2, coarse grid low-precision rapid optimization; s3, fine grid high-precision accurate optimization; s4, outputting and verifying optimal parameters.
More specifically, the coarse mesh and the fine mesh are obtained by the mesh sensitivity analysis in step S1.
More specifically, the coarse mesh is obtained by the fitness function in step S1, and the fitness function may be expressed as:
wherein T is ref St is the exact value of temperature ref For the exact value of the stress, T is the temperature simulated for each grid size, st is the stress simulated for each grid size, T ref For the exact value of the run time, t is the run time required for each grid size simulation, α is the weight of the temperature, β is the weight of the stress, λ is the weight of the run time, fitness represents the function value, max represents the maximum value.
More specifically, step S2 includes the steps of: s21, sampling design parameters by using a first Latin hypercube sampling method; s22, after finite element simulation is carried out by combining coarse grid information, a relation between design parameters and performance parameters is established by using a first neural network; s23, establishing a collaborative design criterion, and optimizing the TSV thermal performance by using a first particle swarm optimization algorithm.
More specifically, the first neural network in step S22 is a GA-BPNN neural network model.
More specifically, the GA-BPNN neural network model may be expressed as:
h 1 ＝g(W 1 U+b 1 )
Thermal/Stress＝g(W 2 h 1 +b 2 )
wherein U is the input of the neural network, W 1 And W is 2 Weight matrix representing input hidden layer and output hidden layer, b 1 And b 2 Respectively representing the deviation values of the input hidden layer and the output hidden layer, h 1 And Thermal/Stress respectively represent the input and output of the output layer, the output performance parameters are temperature and Stress, and g is an activation function.
More specifically, the activation function may be expressed as:where x is the argument and e is the natural logarithm.
More specifically, step S3 includes the steps of: s31, sampling design parameters in the accurate optimal design space by using a second Latin hypercube sampling method; s32, carrying out finite element simulation by combining fine mesh information, and establishing a relation between design parameters and performance parameters by using a second neural network; s33, establishing a collaborative design criterion, and optimizing the TSV thermal performance by using a second particle swarm optimization algorithm.
More specifically, the second Latin hypercube sampling method is the same as the first Latin hypercube sampling method.
More specifically, the second particle swarm optimization algorithm is the same as the first particle swarm optimization algorithm.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a two-stage TSV intelligent thermal cooperative optimization method. Compared with the traditional method, the method reduces the time for acquiring the data set, and then increases the data quantity in the pre-optimization area, so that the final optimization result is more accurate. Specifically, the first stage is to search the TSV peak temperature coarse grid quickly with low precision, and the second stage is to search the TSV peak temperature fine grid accurately with high precision.
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FIG. 1 is a schematic diagram of a two-stage TSV intelligent thermal collaborative optimization method provided by the invention;
fig. 2 is a schematic flow chart of a two-stage TSV intelligent thermal cooperative optimization method provided by the invention.
Detailed Description
In order to make the implementation of the present invention more clear, the following detailed description will be given with reference to the accompanying drawings.
The invention provides a two-stage TSV intelligent thermal cooperative optimization method, which is shown in fig. 1 and 2 and comprises the following steps:
s1, constructing a model and determining the optimal grid size;
and establishing a thermal coupling model of the TSV in the COMSOL by using a finite element method. Grid sensitivity analysis is carried out by utilizing COMSOL, and errors caused by the change of the grid size of the model and calculated time gain are comprehensively evaluated through an evolutionary algorithm; specifically, in the process of changing the grid from small to large, the parameter value is unchanged, the grid corresponding to the critical state corresponding to the parameter value when the parameter value is changed from unchanged to changed state is the fine grid in the embodiment, the solving precision is high, the speed is low, and the required time is long; in the process of continuously enlarging the grid, selecting a coarse grid with larger size according to the Fitness function Fitness, wherein the solving precision is low, the speed is high, and the required time is short; therefore, the aim of distinguishing solving precision according to the size of the grid is fulfilled, and the overall optimization process time is shorter. The range of typical grid variation is from one tenth of the smallest design parameter value within the design parameter range as a starting point, up to three to five times this value. Based on the analysis result, establishing a comprehensive evaluation criterion of model errors and calculation time, selecting the minimum grid size of the Fitness function Fitness, wherein the grid size is larger, the solving precision is lower, and the solving time is shorter; the larger mesh size is used for finite element simulation in the fast optimization process in step S2. More specifically, the evaluation method of the grid and the calculation time, that is, the fitness function expression is as follows:
the method comprises the steps that as the size of a grid is changed, the corresponding maximum parameter value is a reference value, namely an accurate value, namely a critical value of the parameter value starting to change in the process of changing from small to large of the grid, the critical value is represented by a subscript ref, and a parameter without the subscript represents an imitation value; specifically T ref St is the exact value of temperature ref For the exact value of the stress, T is the temperature simulated for each grid size, st is the stress simulated for each grid size, T ref For the exact value of the run time, t is the run time required for each grid size simulation, α is the weight of the temperature, β is the weight of the stress, and λ is the weight of the run time. The Fitness function Fitness minimum means that the combination of error and calculation speed combination tradeoffs is optimal. Therefore, coarse grid information with larger grid size required by finite element simulation in the rapid optimization process can be determined.
S2, coarse grid low-precision rapid optimization;
sampling combinations of design parameters in a design space by a Latin hypercube sampling method (LHS) in the entire design space; the coarse grid information with larger grid size obtained in the step S1 is combined, and the relation between the design parameter and the performance parameter is obtained through finite element simulation, and the method of the invention can increase the simulation speed by sacrificing the finite element simulation precision through enlarging the grid size, thereby increasing the speed of obtaining training data, and then establishing the relation between the design parameter and the performance parameter by utilizing a neural network; and by combining with TSV peak temperature optimization criteria, the TSV peak temperature is primarily and rapidly optimized in the whole design space by using a population optimization algorithm, so that the design space range is reduced. The method comprises the following specific steps:
s21, sampling design parameters by using a first Latin hypercube sampling method;
peak temperature design parameters of the TSV array, including via radius, via pitch, height, offset angle, and oxide thickness were obtained using a first Latin Hypercube Sampling (LHS) design method, as shown in table 1. The sampling method samples uniformly in the whole design space.
Table 1:
s22, after finite element simulation is carried out by combining coarse grid information, a relation between design parameters and performance parameters is established by using a first neural network;
and (3) performing finite element simulation on the design parameter combination generated by the LHS by utilizing the COMSOL, wherein coarse grid information with larger grid size obtained in the step (S1) is required to be combined in the finite element simulation process, specifically, the coarse grid information and the design parameters are input, and corresponding performance parameters are output, namely, a data set of the design parameters and the performance parameters is obtained. And training the relationship between the obtained design parameters and the performance parameters by using the first neural network model. The first neural network model is a GA-BPNN neural network model, the hidden layer number of the neural network is 9, and the GA-BPNN neural network model can be expressed as:
h 1 ＝g(W 1 U+b 1 )
Thermal/Stress＝g(W 2 h 1 +b 2 )
wherein U is the input of the neural network, W 1 And W is 2 Weight matrix representing input hidden layer and output hidden layer, b 1 And b 2 Respectively representing the deviation values of the input hidden layer and the output hidden layer, h 1 And Thermal/Stress respectively represent the input and output of the output layer, and the output performance parameters are temperature and Stress. g is an activation function, which can be expressed as:
s23, establishing a collaborative design criterion, and optimizing the TSV thermal performance by using a first particle swarm optimization algorithm.
In order to avoid the influence caused by different orders of magnitude of performance parameters, the peak temperature is normalized, and the objective function of the TSV array thermodynamic collaborative optimization design criterion is as follows:
wherein alpha is 1 、β 1 The heat radiation performance T and the stress performance St are weighted respectively, des represents the expected value of the corresponding performance parameter, and max and min are the maximum value and the minimum value of the corresponding performance parameter respectively. The design criteria comprises two items, wherein the first item represents temperature, the second item represents stress, and the reflected design criteria have synergistic optimization effect.
Optimizing the TSV thermal performance by using a first Particle Swarm (PSO) optimization algorithm, and updating the PSO optimization algorithm iteratively as follows:
v i (t+1)＝w(iter)v i (t)+c 1 r 1 (p i -x i (t))+c 2 r 2 (p g -x i (t))
x i (t+1)＝x i (t)+v i (t+1)
wherein w is a standard weight; p is p i And p g Is the previous best position for the i-th particle and the global particle. c 1 And c 2 P is respectively i And p g Weights of (2); r is (r) 1 And r 2 Is a random number. item is the current iteration number of the algorithm; ter (iter) max The maximum iteration number; w (w) max And w min Respectively the maximum value and the minimum value of the inertia weight, v i Representation ofSpeed of the ith particle, x i The position of the i-th particle is indicated, and t is the current time. And the method independently runs for more than 30 times, performs preliminary optimization, reduces the design space of the design parameters according to the optimization result, and obtains the accurate optimization design space.
S3, fine grid high-precision accurate optimization;
and in the precise optimization stage, the design space is reduced, and re-optimization is performed in the precise optimization design space obtained in the step S23. In the reduced design space, the combination of design parameters is continuously sampled through LHS, then data is obtained through accurate finite element simulation, then a new neural network is established by using a new data set, and the mapping relation between the design parameters and the performance parameters in the pre-optimized area is constructed. And then, combining the TSV peak temperature optimization criterion in the rapid optimization, and carrying out optimization again by using a population optimization algorithm to obtain final performance optimization parameters. The method comprises the following specific steps:
s31, sampling design parameters in the accurate optimal design space by using a second Latin hypercube sampling method;
and obtaining peak temperature design parameters of the TSV array by adopting a second Latin hypercube sampling method, wherein the peak temperature design parameters comprise the radius of the through silicon vias, the distance between the through silicon vias, the height, the offset angle and the thickness of the oxide layer. Therefore, LHS sampling is performed again in a smaller design space, the sampling process is uniform, but the design space is smaller, so that the number of samples in the unit space is more, namely, the sampling density in the unit space is larger, the optimization accuracy can be effectively improved, and the optimization result is optimal.
S32, carrying out finite element simulation by combining fine mesh information, and establishing a relation between design parameters and performance parameters by using a second neural network;
and (3) performing finite element simulation on the design parameter combination generated by the LHS by utilizing the COMSOL, wherein in the finite element simulation process, fine grid information with smaller grid size obtained in the step S1 is required to be combined, specifically, the fine grid information and the design parameters obtained by sampling in the step S31 are input, and corresponding performance parameters are output, namely, new design parameters and a data set of the performance parameters are obtained. The new second neural network model is utilized to train the relationship between the obtained design parameters and the performance parameters. The second neural network model is a GA-BPNN neural network model, the hidden layer number of the neural network is 9, and the GA-BPNN neural network model can be expressed as:
h 3 ＝g(W 3 U+b 3 )
Thermal/Stress＝g(W 4 h 3 +b 4 )
wherein U is the input of the neural network, W 3 And W is 4 Weight matrix representing input hidden layer and output hidden layer, b 3 And b 4 Respectively representing the deviation values of the input hidden layer and the output hidden layer, h 3 And Thermal/Stress respectively represent the input and output of the output layer, the output performance parameters are temperature and Stress, g is an activation function, and can be expressed as:
s33, establishing a collaborative design criterion, and optimizing the TSV thermal performance by using a second particle swarm optimization algorithm.
In order to avoid the influence caused by different orders of magnitude of performance parameters, the peak temperature is normalized, and the objective function of the TSV array thermodynamic collaborative optimization design criterion is as follows:
wherein alpha is 2 、β 2 The heat radiation performance T and the stress performance St are weighted respectively, des represents the expected value of the corresponding performance parameter, and max and min are the maximum value and the minimum value of the corresponding performance parameter respectively. The design criteria comprises two items, wherein the first item represents temperature, the second item represents stress, and the reflected design criteria have synergistic optimization effect.
Optimizing the TSV thermal performance by using a second PSO optimization algorithm, and updating the PSO optimization algorithm iteratively as follows:
v i (t+1)＝w(iter)v i (t)+c 3 r 3 (p i -x i (t))+c 4 r 4 (p g -x i (t))
x i (t+1)＝x i (t)+v i (t+1)
wherein w is a standard weight; p is p i And p g Is the previous best position for the i-th particle and the global particle. c 3 And c 4 P is respectively i And p g Weights of (2); r is (r) 3 And r 4 Is a random number. item is the current iteration number of the algorithm; ter (iter) max The maximum iteration number; w (w) max And w min Respectively the maximum value and the minimum value of the inertia weight, v i Represents the speed of the ith particle, x i The position of the i-th particle is indicated, and t is the current time. And (5) performing independent optimization for more than 30 times again, and performing accurate optimization to obtain optimal design parameters and performance parameters.
S4, outputting and verifying optimal parameters.
When the error between the design parameters optimized independently for 30 times is less than 10 -2 Judging convergence, and judging non-convergence if the convergence is larger than the convergence; if the design parameters are not converged, further carrying out accurate optimization through design criteria and an evolutionary algorithm, and if the design parameters are converged, deriving optimal design parameters and performance parameters. Finally, verifying through COMSOL finite element simulation according to the optimized result; and (3) respectively inputting the optimized design parameters into the finite element model and the neural network established in the step (S3) for simulation, and comparing the corresponding performance parameters output through the finite element simulation with the performance parameters output by the neural network, wherein the result is considered to be reliable if the error is less than 3%.
In summary, the design space is reduced according to the rapid optimization result to form an accurate optimization space, so that different grids are used at different stages, and different solving precision and sensitivity are corresponding; in the formed accurate optimization space, uniform sampling and accurate solving are performed, and accurate optimization is performed, so that the sampling density in the accurate optimization space is higher, namely, the accurate optimization with lower speed is performed near an optimal result, and finally, the optimal design parameters and performance parameters are obtained, and the overall optimization time is reduced. Compared with the traditional method, the method reduces the time for acquiring the data set, and then increases the data quantity in the pre-optimization area, so that the final optimization result is more accurate, and therefore, the method has the advantages of short optimization time and high efficiency.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. The intelligent thermal collaborative optimization method for the two-stage TSV is characterized by comprising the following steps of:
s1, constructing a model and determining the optimal grid size;
s2, coarse grid low-precision rapid optimization;
s3, fine grid high-precision accurate optimization;
s4, outputting and verifying optimal parameters.
2. The two-stage TSV intelligent thermal collaborative optimization method according to claim 1, wherein the coarse grid and the fine grid are obtained through the grid sensitivity analysis in the step S1.
3. The two-stage TSV intelligent thermal collaborative optimization method according to claim 2, wherein the coarse mesh is obtained through the fitness function in step S1, and the fitness function can be expressed as:
wherein T is ref St is the exact value of temperature ref For the exact value of the stress, T is the temperature simulated for each grid size, st is the stress simulated for each grid size, T ref For the exact value of the run time, t is the run time required for each grid size simulation, α is the weight of the temperature, β is the weight of the stress, λ is the weight of the run time, fitness represents the function value, max represents the maximum value.
4. The two-stage TSV intelligent thermal collaborative optimization method according to claim 3, wherein the step S2 includes the steps of:
s21, sampling design parameters by using a first Latin hypercube sampling method;
s22, after finite element simulation is carried out by combining coarse grid information, a relation between design parameters and performance parameters is established by using a first neural network;
s23, establishing a collaborative design criterion, and optimizing the TSV thermal performance by using a first particle swarm optimization algorithm.
5. The two-stage TSV intelligent thermal collaborative optimization method according to claim 4, wherein the first neural network in the step S22 is a GA-BPNN neural network model.
6. The two-stage TSV intelligent thermal synergy optimization method according to claim 5, wherein the GA-BPNN neural network model can be expressed as:
h 1 ＝g(W 1 U+b 1 )
Thermal/Stress＝g(W 2 h 1 +b 2 )
wherein U is the input of the neural network, W 1 And W is 2 Weight matrix representing input hidden layer and output hidden layer, b 1 And b 2 Respectively representing the deviation values of the input hidden layer and the output hidden layer, h 1 And Thermal/Stress respectively represent the input and output of the output layer, the output performance parameters are temperature and Stress, and g is an activation function.
7. The two-stage TSV intelligent thermal co-optimization method according to claim 6 wherein the activation function can be expressed as:where x is the argument and e is the natural logarithm.
8. The two-stage TSV intelligent thermal synergy optimization method according to claim 1 or 7, wherein the step S3 includes the steps of:
s31, sampling design parameters in the accurate optimal design space by using a second Latin hypercube sampling method;
s32, carrying out finite element simulation by combining fine mesh information, and establishing a relation between design parameters and performance parameters by using a second neural network;
s33, establishing a collaborative design criterion, and optimizing the TSV thermal performance by using a second particle swarm optimization algorithm.
9. The two-stage TSV intelligent thermal synergy optimization method of claim 8 wherein the second latin hypercube sampling method is the same as the first latin hypercube sampling method.
10. The two-stage TSV intelligent thermal synergy optimization method of claim 9 wherein the second particle swarm optimization algorithm is the same as the first particle swarm optimization algorithm.
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