WO2023115815A1 - Procédé de résolution de transport thermique de phonons au niveau d'une interface, et support d'enregistrement - Google Patents

Procédé de résolution de transport thermique de phonons au niveau d'une interface, et support d'enregistrement Download PDF

Info

Publication number
WO2023115815A1
WO2023115815A1 PCT/CN2022/095366 CN2022095366W WO2023115815A1 WO 2023115815 A1 WO2023115815 A1 WO 2023115815A1 CN 2022095366 W CN2022095366 W CN 2022095366W WO 2023115815 A1 WO2023115815 A1 WO 2023115815A1
Authority
WO
WIPO (PCT)
Prior art keywords
phonon
temperature
deviation
intensity
pseudo
Prior art date
Application number
PCT/CN2022/095366
Other languages
English (en)
Chinese (zh)
Inventor
冉鑫
Original Assignee
苏州浪潮智能科技有限公司
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 苏州浪潮智能科技有限公司 filed Critical 苏州浪潮智能科技有限公司
Publication of WO2023115815A1 publication Critical patent/WO2023115815A1/fr

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation

Definitions

  • the present application relates to the technical field of heat transfer, in particular to a method and a storage medium for solving the heat transport of phonons at an interface.
  • the heat dissipation problem of electronic devices has become a major obstacle restricting its further development.
  • the research on the heat transport mechanism of phonons in semiconductors can provide effective guidance for the heat dissipation optimization design of electronic devices.
  • the research methods mainly include theoretical calculation, experimental research and numerical simulation.
  • the discrete coordinate method is an important numerical tool for studying phonon heat transport in semiconductors.
  • the discrete coordinate method has obvious advantages for the simulation of mesoscopic scale systems with simple geometric shapes. Its algorithm is simple to implement and the simulation accuracy is high.
  • the numerical algorithm framework of the phonon discrete coordinate method is still not perfect.
  • the phonon discrete coordinate method considering the actual dispersion relationship is mainly divided into two categories: numerical algorithms based on linearized equations under small temperature differences and numerical algorithms based on nonlinear equations under arbitrary temperature differences.
  • the two types of numerical algorithms can further consider steady-state and transient situations, corresponding to space-domain and time-space domain algorithms.
  • Numerical algorithms based on linear Boltzmann equations are simpler and more efficient than those based on nonlinear Boltzmann equations.
  • Using the discrete coordinate method it is possible to simulate the heat transport process of phonons in a system without an interface or with an interface. Unlike the former, the latter needs to consider the information exchange mechanism of phonons at the interface in the materials on both sides of the interface. The process is more complicated.
  • the inventor realizes that at present, for the phonon discrete coordinate method based on the linearization equation, the space-domain and space-time domain algorithm framework of the discrete coordinate method without considering the interface system, and the space-domain algorithm framework of the discrete coordinate method considering the interface system have been established , but the existing time-space domain algorithm framework of the discrete coordinate method considering the interface system still needs to be further improved to meet the increasingly urgent numerical simulation needs of the study of phonon heat transport in semiconductors.
  • a method for solving phonon heat transport at an interface comprising the following steps: step S1, initializing setting parameters and system parameters; step S2, obtaining phonon deviation strength based on system parameters; step S3, based on linear Bohr Zeman equation and phonon interface conditions, update the phonon deviation strength iteratively, and obtain the corresponding temperature, pseudo temperature and heat flow based on any phonon deviation strength; step S4, obtain the temperature corresponding to the current phonon deviation strength and the previous phonon deviation strength The temperature difference corresponding to the deviation intensity, and define the difference as a relative error; step S5, compare the relative error with the preset convergence error, if the relative error is not greater than the convergence error, then output the current phonon deviation intensity corresponding to temperature, pseudo temperature and heat flow.
  • the method further includes: step S6, obtaining the calculation time length for iteratively updating the phonon deviation strength, and defining the calculation time length as the first calculation time length; step S7, if the first calculation time length is less than the preset total calculation time duration, then continue to execute steps S3, S4, S5, S6 and S7; otherwise, output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity.
  • the setting parameters include: space step size, system scale, time step size, total calculation time and convergence error; system parameters include: temperature and pseudo temperature; phonon deviation strength includes: based on phonon strength acquisition The obtained first bias strength and the obtained second bias strength are acquired based on the phonon pseudo-balance strength.
  • step S2 specifically includes: step S21, the initial value of the set temperature is T 0 , based on the initial value of the temperature, the obtained phonon intensity is:
  • I ⁇ , p is the phonon intensity
  • v g is the phonon group velocity
  • ⁇ is the phonon angular frequency
  • p is the phonon branch
  • f ⁇ , p is the phonon distribution
  • D is the phonon density of state
  • D( ⁇ , p) means that the phonon branch is p
  • the phonon density of state at which the phonon angular frequency is ⁇ ; step S22, based on the phonon intensity, the obtained phonon reference equilibrium intensity is:
  • step S23 based on the phonon intensity and the phonon reference equilibrium intensity, obtain the first deviation intensity:
  • ⁇ ⁇ , p is the first deviation intensity
  • I ⁇ , p is the phonon intensity
  • i ⁇ is the phonon reference equilibrium strength
  • step S24 setting the initial value of the pseudo-temperature equal to the initial value of the equilibrium value is T 0 , based on the initial value of the pseudo-temperature, the pseudo-equilibrium strength of the obtained phonon is:
  • step S25 based on the phonon intensity and the pseudo-equilibrium intensity of the phonon, obtain the second deviation intensity:
  • the linear Boltzmann equation is:
  • ⁇ ⁇ , p is the first deviation intensity, is the second deviation strength
  • ⁇ ⁇ , p is the phonon relaxation time
  • ⁇ is the phonon angular frequency
  • p is the phonon branch
  • v g is the phonon group velocity
  • v g ( ⁇ , p) is the phonon branch as The phonon group velocity of p and phonon angular frequency ⁇ ;
  • a and B represent two materials respectively
  • ⁇ is the angle between the interface normal vector and the group velocity
  • the positive direction of the interface normal is from material A to material B
  • ⁇ AB ( ⁇ ) and ⁇ AB ( ⁇ ) are respectively Spectrum interface penetration coefficient from material A to material B and material B to material A
  • ⁇ B, ⁇ , p is the first deviation intensity of material B
  • ⁇ A, ⁇ , p is the first deviation intensity of material A.
  • obtaining the corresponding temperature, pseudo temperature and heat flow based on any phonon deviation intensity specifically includes: step S31, based on the basic definition of phonon deviation intensity and temperature, obtaining the linear expression of temperature:
  • T ref is a constant reference temperature
  • ⁇ is a polar coordinate
  • ⁇ max represents the maximum phonon angular frequency of the phonon branch p
  • v g is the phonon group velocity
  • ⁇ ⁇ p is the first deviation strength
  • spectral volume heat capacity that is, the volume heat capacity of each phonon branch and unit phonon angle frequency range
  • Step S32 based on the basic definition of phonon deviation strength and pseudo temperature, obtain the linear expression of pseudo temperature:
  • T pse is the pseudo temperature
  • ⁇ ⁇ , p is the phonon relaxation time
  • pseudo temperature the basic definition of pseudo temperature
  • Step S33 based on the phonon deviation intensity, obtain the linear expression of the heat flow:
  • step S5 specifically includes: step S51, obtaining the relative error between the temperature corresponding to the current phonon deviation intensity and the temperature corresponding to the previous phonon deviation intensity based on the following formula:
  • ⁇ represents the relative error
  • n represents the spatial unit index
  • N represents the total number of spatial units
  • i represents the iteration number index
  • T is the temperature
  • Step S52 if the relative error is not greater than the convergence error, then output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity.
  • step S5 specifically includes:
  • Step S53 Obtain the difference between the heat flow corresponding to the current phonon deviation intensity and the heat flow corresponding to the previous phonon deviation intensity based on the following formula, and define the difference as a relative error:
  • ⁇ is the relative error
  • n is the spatial unit index
  • N is the total number of spatial units
  • i is the iteration number index
  • q is the heat flow
  • Step S54 comparing the relative error with the preset convergence error, and if the relative error is not greater than the convergence error, then output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity.
  • the corresponding temperature, pseudo temperature and heat flow are obtained based on any phonon deviation intensity, including:
  • Integral summation is performed based on any phonon deviation intensity to obtain the heat flow corresponding to any phonon deviation intensity.
  • One or more non-volatile computer-readable storage media storing computer-readable instructions, when the computer-readable instructions are executed by one or more processors, one or more processors are made to execute the method provided by any one of the above-mentioned embodiments Steps in a method to solve for phonon heat transport at an interface.
  • FIG. 1 is an internal structural diagram of a computer device provided according to one or more embodiments of the present application.
  • Fig. 2 is a flow chart of a method for solving phonon heat transport at an interface according to one or more embodiments of the present application
  • Fig. 3 is a flow chart of a method for solving phonon heat transport at an interface according to one or more embodiments of the present application
  • FIG. 4 is a schematic structural view of a double-layer film provided according to one or more embodiments of the present application.
  • Fig. 5 is a temperature evolution experiment result diagram of a double-layer film provided according to one or more embodiments of the present application.
  • Fig. 6 is a graph showing experimental results of heat flow evolution of a double-layer thin film according to one or more embodiments of the present application.
  • the computer device can be a server, and its internal structure diagram can be shown in FIG. 1 .
  • the computer device includes a processor, memory, network interface and database connected by a system bus. Wherein, the processor of the computer device is used to provide calculation and control capabilities.
  • the memory of the computer device includes a non-volatile storage medium and an internal memory.
  • the non-volatile storage medium stores an operating system, computer readable instructions and a database.
  • the internal memory provides an environment for the execution of the operating system and computer readable instructions in the non-volatile storage medium.
  • the database of the computer equipment is used to store data such as setting parameters and system parameters.
  • the network interface of the computer device is used to communicate with an external terminal via a network connection.
  • the computer readable instructions when executed by the processor, implement the method for solving the phonon heat transport at the interface.
  • the server may be implemented by an independent server or a server cluster composed of multiple servers.
  • FIG. 2 is a flow chart of the method in Embodiment 1.
  • Step S1 initialize setting parameters; wherein, the setting parameters include space step, system scale, time step, total calculation time and convergence error; system scale is the system's spatial scale, such as: system length, width and height. Because it only involves one-dimensional space, that is, this application only considers the change of system parameters in the thickness direction of the experimental material, that is, if only the change of the system in the length of the experimental material is considered, it is assumed that the width and height of the experimental material are Unlimited.
  • the total time step is the total simulation time length when calculating the phonon heat transport of the experimental material at the interface, and the time step is the sampling point in the total time step, that is to say, The total time step is composed of several time steps.
  • the experiment simulates the temperature change of the experimental material from time 0 to 1000 picoseconds (ps), where the time length of 1000 ps is the total time step.
  • 1000ps is divided into 1000 sampling points, that is, one sampling is performed at 1ps, then 1ps is the first sampling point, and this sampling point is the time step.
  • the system parameters include phonon intensity and phonon pseudo-equilibrium intensity. It should be understood that in order to avoid the divergence of calculation results and speed up the convergence speed, those skilled in the art should use the average value of phonon mean free path and relaxation time as a reference when setting the space step size and time step size. Try to make the space step and time step smaller than the average value of phonon mean free path and relaxation time.
  • Step S2 setting the initial value of phonon intensity and phonon pseudo-balance intensity value; this step S2 specifically includes: based on the initial value of temperature, obtaining its corresponding phonon intensity, phonon reference temperature and first deviation intensity; The initial value of the temperature is used to obtain the corresponding phonon pseudo-equilibrium intensity and the second deviation intensity.
  • obtaining its corresponding phonon intensity, phonon reference temperature and first deviation intensity specifically includes the following steps: Step S21, setting the initial value of temperature to T 0 , In the case where the initial value of the known temperature is T0 , the phonon intensity is solved based on the following formula:
  • I ⁇ , p is the phonon intensity
  • v g is the phonon group velocity
  • ⁇ is the phonon angular frequency
  • p is the phonon branch
  • f ⁇ is the phonon distribution
  • D is the phonon density of state
  • D( ⁇ , p) means that the phonon branch is p and Phonon density of states at phonon angular frequency ⁇ .
  • Step S22 based on the phonon intensity, obtain the phonon reference equilibrium intensity as:
  • Step S23 based on the phonon strength and the phonon reference balance strength, obtain the first deviation strength:
  • ⁇ ⁇ , p is the first deviation intensity
  • I ⁇ , p is the phonon intensity
  • obtaining the corresponding phonon pseudo-balance intensity and the second deviation intensity specifically includes:
  • Step S24 set the initial value of the pseudo-temperature equal to the initial value of the equilibrium value as T 0 , that is, assume that the phonon temperature and the phonon pseudo-temperature value are both T 0 , based on the initial value of the pseudo-temperature, obtain the acoustic
  • the sub-pseudo-balance strength is:
  • Step S25 based on the phonon strength and the phonon pseudo-balance strength, obtain the second deviation strength:
  • Step S3 obtaining the first phonon intensity based on the linear Boltzmann equation. That is, the phonon intensity acquired in step S21 is iteratively updated based on the linear Boltzmann equation, and the acquired iteratively updated phonon intensity is defined as the first phonon intensity.
  • obtaining the first phonon intensity based on the Boltzmann equation specifically includes: the linear Boltzmann equation is:
  • ⁇ ⁇ , p is the first deviation intensity, is the second deviation strength
  • ⁇ ⁇ , p is the phonon relaxation time
  • ⁇ is the phonon angular frequency
  • p is the phonon branch
  • v g is the phonon group velocity
  • v g ( ⁇ , p) is the phonon branch as The phonon group velocity of p and phonon angular frequency ⁇ .
  • the differential format is used for both time and space differentiation.
  • the total calculation time is divided into several time steps, and the thermal transport of phonons at the interface is solved based on any time step, it is necessary to consider the mutual exchange of phonon information at the interface situation, that is to say, in the actual experimental process, the interface conditions need to be considered, and the interface conditions are:
  • a and B represent two materials respectively
  • ⁇ is the angle between the interface normal vector and the group velocity
  • the positive direction of the interface normal is from material A to material B
  • ⁇ AB ( ⁇ ) and ⁇ BA ( ⁇ ) are respectively Spectrum interface penetration coefficient from material A to material B and material B to material A
  • ⁇ B, ⁇ , p is the first deviation intensity of material B
  • ⁇ A, ⁇ , p is the first deviation intensity of material A.
  • Step S4 obtaining temperature, pseudo temperature and heat flow based on the first phonon intensity. Specifically include the following steps:
  • Step S31 based on the basic definition of phonon deviation intensity and temperature, obtain the linear expression of temperature:
  • T ref is a constant reference temperature
  • ⁇ is a polar coordinate
  • ⁇ max represents the maximum phonon angular frequency of the phonon branch p
  • v g is the phonon group velocity
  • ⁇ ⁇ p is the first deviation strength
  • spectral volume heat capacity that is, the volume heat capacity of each phonon branch and unit phonon angle frequency range
  • Step S32 based on the basic definition of phonon deviation strength and pseudo temperature, obtain the linear expression of pseudo temperature:
  • T pse is the pseudo temperature, ⁇ ⁇ , p is the phonon relaxation time;
  • pseudo temperature the basic definition of pseudo temperature
  • Step S33 based on the phonon deviation intensity, obtain the linear expression of the heat flow:
  • Step S5 obtaining the relative error of two similar temperatures. Specifically include the following steps:
  • Step S51 obtain the relative error between the temperature corresponding to the current phonon deviation intensity and the temperature corresponding to the previous phonon deviation intensity based on the following formula:
  • ⁇ represents the relative error
  • n represents the spatial unit index
  • N represents the total number of spatial units
  • i represents the iteration number index
  • T is the temperature
  • Step S52 if the relative error is not greater than the convergence error, output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity, and continue to judge whether the calculation time is greater than or equal to the final evolution time. That is, it is judged whether the current calculation time exceeds the preset total calculation time.
  • step S52 in response to the relative error being not greater than the convergence error, output the temperature, pseudo temperature, and heat flow corresponding to the current phonon deviation intensity, and continue to judge whether the calculation time is greater than or equal to the final evolution time.
  • the output temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity here are the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity output at the current time step. Because the total calculation time is composed of multiple time steps, the purpose of judging whether the current calculation time exceeds the preset total calculation time is to proceed to the next time step if the current calculation time does not exceed the preset total calculation time Calculation of long temperature, pseudo temperature and heat flow.
  • step S5 the relative error of two close temperatures is acquired. Specifically, the following steps may also be included:
  • Step S53 Obtain the difference between the heat flow corresponding to the current phonon deviation intensity and the heat flow corresponding to the previous phonon deviation intensity based on the following formula, and define the difference as a relative error:
  • ⁇ is the relative error
  • n is the spatial unit index
  • N is the total number of spatial units
  • i is the iteration number index
  • q is the heat flow
  • Step S54 compare the relative error with the preset convergence error, if the relative error is not greater than the convergence error, output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity, and continue to judge whether the calculation time is greater than or equal to the final evolution time . That is, it is judged whether the current calculation time exceeds the preset total calculation time.
  • step S54 in response to the relative error being not greater than the convergence error, output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity, and continue to judge whether the calculation time is greater than or equal to the final evolution time.
  • the output temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity here are the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity output at the current time step. Because the total calculation time is composed of multiple time steps, the purpose of judging whether the current calculation time exceeds the preset total calculation time is to proceed to the next time step if the current calculation time does not exceed the preset total calculation time Calculation of long temperature, pseudo temperature and heat flow.
  • continuing to judge whether the calculation time is greater than or equal to the final evolution time specifically includes the following steps:
  • Step S6 obtaining the calculation duration for iteratively updating the phonon deviation strength, and defining the calculation duration as the first calculation duration;
  • Step S7 If the first calculation duration is less than the preset total calculation duration, continue to execute steps S3, S4, S5, S6 and S7; otherwise, output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity.
  • step S7 in response to the first calculation duration being less than the preset total calculation duration, continue to execute steps S3, S4, S5, S6 and S7; in response to the first calculation duration being not less than the preset total calculation duration , output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation strength.
  • step S3, S4, S5, S6 and S7 that is, to solve the heat transport of phonons at the phonons of the next time step; otherwise, if If the first calculation duration is greater than or equal to the preset total calculation duration, the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity are output.
  • the first calculation duration is less than the preset total calculation duration, then continue to execute steps S3, S4, S5, S6 and S7, that is, perform the next iterative update of the first phonon intensity, that is, the current
  • the first phonon intensity is brought into step S3, and the current first phonon intensity is iteratively updated to obtain the first phonon intensity again until the first calculation duration is greater than or equal to the preset total calculation duration.
  • no specific values are given for the preset setting parameters and system parameters such as convergence error, total calculation time, and time step. Those skilled in the art can Reasonable selection according to the situation, only need to meet the relevant requirements in this embodiment.
  • This embodiment can directly, accurately and efficiently solve the heat transport of phonons at the inner interface of the semiconductor, and ensure the accuracy of the solution results to the greatest extent.
  • FIG. 3 is a flow chart of the method in the second embodiment.
  • the method for solving the heat transport of phonons at the interface in this embodiment includes the following steps: step S1, initialize setting parameters and system parameters; step S2, obtain the phonon deviation intensity based on the system parameters; step S3, based on the linear Bohr Zeman equation and phonon interface conditions, update the phonon deviation strength iteratively, and obtain the corresponding temperature, pseudo temperature and heat flow based on any phonon deviation strength; step S4, obtain the temperature corresponding to the current phonon deviation strength and the previous phonon deviation strength The temperature difference corresponding to the deviation intensity, and define the difference as a relative error; step S5, compare the relative error with the preset convergence error, if the relative error is not greater than the convergence error, then output the current phonon deviation intensity corresponding to Temperature, Pseudo-Temperature and Heat Flow. Specifically, in the above step S5, in response to the fact that the relative error is not greater than the convergence error, the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity are output.
  • the method further includes: step S6, obtaining the calculation duration for iteratively updating the phonon deviation strength, and defining the calculation duration as the first calculation duration; step S7, if the first calculation duration is less than the preset total calculation duration, Then continue to execute steps S3, S4, S5, S6 and S7; otherwise, output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation intensity.
  • step S7 in response to the first calculation duration being less than the preset total calculation duration, continue to execute steps S3, S4, S5, S6 and S7; in response to the first calculation duration being not less than the preset total calculation duration , output the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation strength.
  • the setting parameters include: space step size, system scale, time step size, total calculation time and convergence error; system parameters include: temperature and pseudo temperature; phonon deviation strength includes: obtained based on phonon strength The first bias strength and the second bias strength obtained based on the phonon pseudo-equilibrium strength.
  • step S2 specifically includes: step S21, the initial value of the set temperature is T 0 , based on the initial value of the temperature, the obtained phonon intensity is:
  • I ⁇ , p is the phonon intensity
  • v g is the phonon group velocity
  • ⁇ is the phonon angular frequency
  • p is the phonon branch
  • f ⁇ , p is the phonon distribution
  • D is the phonon density of state
  • D( ⁇ , p) means that the phonon branch is p and Phonon density of states with phonon angular frequency ⁇ ;
  • Step S22 based on the phonon intensity, obtain the phonon reference equilibrium intensity as:
  • Step S23 based on the phonon strength and the phonon reference balance strength, obtain the first deviation strength:
  • ⁇ ⁇ , p is the first deviation intensity
  • I ⁇ , p is the phonon intensity, is the phonon reference equilibrium strength
  • Step S24 set the initial value of the pseudo-temperature equal to the initial value of the equilibrium value as T 0 , based on the initial value of the pseudo-temperature, obtain the pseudo-equilibrium strength of the phonon as:
  • Step S25 based on the phonon strength and the phonon pseudo-balance strength, obtain the second deviation strength:
  • the linear Boltzmann equation is:
  • ⁇ ⁇ , p is the first deviation intensity, is the second deviation strength, ⁇ ⁇ , p is the phonon relaxation time, ⁇ is the phonon angular frequency, p is the phonon branch, v g is the phonon group velocity, v g ( ⁇ , p) is the phonon branch as The phonon group velocity of p and phonon angular frequency ⁇ ;
  • the interface conditions are:
  • a and B represent two materials respectively
  • ⁇ is the angle between the interface normal vector and the group velocity
  • the positive direction of the interface normal is from material A to material B
  • ⁇ AB ( ⁇ ) and ⁇ BA ( ⁇ ) are respectively Spectrum interface penetration coefficient from material A to material B and material B to material A
  • ⁇ B, ⁇ , p is the first deviation intensity of material B
  • ⁇ A, ⁇ , p is the first deviation intensity of material A.
  • obtaining the corresponding temperature, pseudo temperature and heat flow based on any phonon deviation intensity specifically includes: step S31, based on the basic definition of phonon deviation intensity and temperature, obtaining a linear expression of temperature:
  • T ref is a constant reference temperature
  • ⁇ is a polar coordinate
  • ⁇ max represents the maximum phonon angular frequency of the phonon branch p
  • v g is the phonon group velocity
  • ⁇ ⁇ p is the first deviation strength
  • spectral volume heat capacity that is, the volume heat capacity of each phonon branch and unit phonon angle frequency range
  • Step S32 based on the basic definition of phonon deviation strength and pseudo temperature, obtain the linear expression of pseudo temperature:
  • T pse is the pseudo temperature, ⁇ ⁇ , p is the phonon relaxation time
  • pseudo temperature the basic definition of pseudo temperature
  • Step S32 the basic definition of pseudo temperature is:
  • Step S33 based on the phonon deviation intensity, obtain the linear expression of the heat flow:
  • step S5 specifically includes: step S51, obtaining the relative error between the temperature corresponding to the current phonon deviation intensity and the temperature corresponding to the previous phonon deviation intensity based on the following formula:
  • ⁇ represents the relative error
  • n represents the spatial unit index
  • N represents the total number of spatial units
  • i represents the iteration number index
  • T is the temperature
  • step S52 if the relative error is not greater than the convergence error, then output the current phonon deviation intensity corresponding to Temperature, Pseudo-Temperature and Heat Flow.
  • step S5 specifically includes:
  • Step S53 Obtain the difference between the heat flow corresponding to the current phonon deviation intensity and the heat flow corresponding to the previous phonon deviation intensity based on the following formula, and define the difference as a relative error:
  • ⁇ is the relative error
  • n represents the spatial unit index
  • N represents the total number of spatial units
  • i represents the iteration number index
  • q is the heat flow
  • step S54 compare the relative error with the preset convergence error, if the relative error is not greater than Convergence error, the temperature, pseudo temperature and heat flow corresponding to the current phonon deviation strength are output.
  • obtaining the corresponding temperature, pseudo temperature, and heat flow based on any phonon deviation intensity includes: obtaining the temperature corresponding to any phonon deviation intensity based on the basically defined ratio between any phonon deviation intensity and temperature; The ratio of any phonon deviation intensity to the basic definition of pseudo temperature is used to obtain the pseudo temperature corresponding to any phonon deviation intensity; the heat flow corresponding to any phonon deviation intensity is obtained by integral summation based on any phonon deviation intensity.
  • a double-layer thin film is taken as an example, and its one-dimensional unsteady state phonon heat transport is solved.
  • the bilayer film is composed of germanium and silicon with equal thickness, and the film thickness is 120 nanometers.
  • the two ends of the film are isothermal boundaries, which are fixed at 301K and 299K respectively, which meet the requirements of the small temperature difference between the two sides of the interface in this application.
  • the initial temperature inside the film is a uniform temperature of 300K, and the temperature and heat flow gradually tend to steady state.
  • the temperature evolution diagram and heat flow evolution diagram of the above-mentioned double-layer thin film at multiple different time steps obtained based on the Monte Carlo method are used as a reference, based on the traditional method for solving the phonon heat transport at the interface and the solution interface proposed by this application
  • the method of phonon heat transport is used to verify the accuracy of the two methods.
  • the above-mentioned double-layer thin film obtained based on the prior art, the method of the present application and the Monte Carlo method obtained under set parameters A plot of the temperature evolution of the thin film at several different time steps. Specifically include: the initial space step is 0.2 nanometers, the time step is 0.2 ps, the total calculation time is 0.6 nanoseconds, the convergence error is 1*10 -8 , and the initial value of the temperature is 300 Kelvin.
  • the figure includes the temperature evolution curve of the double-layer film with a time step of 6ps, a time step of 48ps and a time step of 600ps, and also includes the method based on the application under any of the above-mentioned time steps .
  • the temperature curves obtained by the three methods at any time step are displayed together , for comparison. As can be seen from Fig.
  • the curve of temperature calculated by the traditional method is quite different from the correct value obtained based on the Monte Carlo method, while the curve of temperature obtained by the method of the present application is different from that obtained based on the Monte Carlo method.
  • the difference between the correct values of is small, which proves that the method for solving the phonon heat transport at the interface of the present application can guarantee the accuracy and precision of the calculation results to the greatest extent.
  • 6 includes the heat flow evolution curve of the double-layer thin film with a time step of 6ps, a time step of 48ps and a time step of 600ps, and also includes the heat flow evolution curve based on the application under any of the above-mentioned time steps.
  • method based on the traditional method of solving the heat transport of phonons at the interface and the heat flow evolution curve of the above-mentioned double-layer film obtained based on the Monte Carlo method, the heat flow curves obtained by the three methods at any time step are shown in together for comparison.
  • the heat flow curve calculated by the traditional method is quite different from the correct value obtained based on the Monte Carlo method, while the heat flow curve obtained by the method of the present application is different from that obtained based on the Monte Carlo method.
  • the difference between the correct values of is small, which proves that the method for solving the phonon heat transport at the interface of the present application can guarantee the accuracy and precision of the calculation results to the greatest extent.
  • the X-axis represents the dimensionless space coordinate, specifically the ratio between the space coordinate and the film thickness
  • the Y-axis of Figure 5 represents the temperature, and the unit is Kelvin
  • the Y-axis of Figure 6 Indicates heat flow in watts per square meter.
  • This embodiment provides one or more non-volatile computer-readable storage media storing computer-readable instructions.
  • the computer-readable instructions are executed by one or more processors, the one or more processors execute any one of the above-mentioned The steps of the method for solving the phonon heat transport at the interface provided in the embodiment.
  • the embodiments in the embodiments of the present application may be provided as methods, systems, or computer-readable instruction products. Therefore, the embodiment of the present application may be in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the embodiments of the present application may adopt computer-readable instruction products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes therein. form.
  • computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • Embodiments of the present application are described with reference to flowcharts and/or block diagrams of methods, devices (systems), and computer-readable instruction products according to embodiments of the present application. It should be understood that each process and/or block in the flowchart and/or block diagram, and a combination of processes and/or blocks in the flowchart and/or block diagram can be implemented by computer-readable instructions. These computer-readable instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device Produce means for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.
  • These computer-readable instructions instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means,
  • the instruction means implements the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.
  • These computer-readable instructions instructions can also be loaded on a computer or other programmable data processing device, so that a series of operational steps are performed on the computer or other programmable device to produce a computer-implemented process, thereby
  • the executed instructions provide steps for implementing the functions specified in the procedure or procedures of the flowchart and/or the block or blocks of the block diagrams.

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Investigating Or Analyzing Materials Using Thermal Means (AREA)
  • Thin Film Transistor (AREA)

Abstract

La présente invention concerne un procédé de résolution de transport thermique de phonons au niveau d'une interface, et un support d'enregistrement. Le procédé consiste à : initialiser les paramètres définis et les paramètres du système ; acquérir une intensité de déviation des phonons sur la base des paramètres du système ; mettre à jour itérativement l'intensité de déviation des phonons sur la base d'une équation linéaire de Boltzmann et d'une condition d'interface des phonons, et obtenir une température, une pseudo-température et un flux de chaleur correspondants sur la base de toute intensité de déviation des phonons ; acquérir la différence entre la température correspondant à l'intensité de déviation des phonons actuelle et la température correspondant à l'intensité de déviation des phonons précédente, et définir la différence comme une erreur relative ; et comparer l'erreur relative à une erreur de convergence prédéfinie, et si l'erreur relative n'est pas supérieure à l'erreur de convergence, émettre la température, la pseudo-température et le flux de chaleur correspondant à l'intensité de déviation des phonons actuelle.
PCT/CN2022/095366 2021-12-24 2022-05-26 Procédé de résolution de transport thermique de phonons au niveau d'une interface, et support d'enregistrement WO2023115815A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202111594201.5 2021-12-24
CN202111594201.5A CN113987841B (zh) 2021-12-24 2021-12-24 一种求解界面处声子热输运的方法和存储介质

Publications (1)

Publication Number Publication Date
WO2023115815A1 true WO2023115815A1 (fr) 2023-06-29

Family

ID=79734210

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2022/095366 WO2023115815A1 (fr) 2021-12-24 2022-05-26 Procédé de résolution de transport thermique de phonons au niveau d'une interface, et support d'enregistrement

Country Status (2)

Country Link
CN (1) CN113987841B (fr)
WO (1) WO2023115815A1 (fr)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113987841B (zh) * 2021-12-24 2022-04-19 苏州浪潮智能科技有限公司 一种求解界面处声子热输运的方法和存储介质

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070230135A1 (en) * 2006-03-31 2007-10-04 International Business Machines Corporation Heat transfer control structures using thermal phonon spectral overlap
CN101760183A (zh) * 2009-12-30 2010-06-30 哈尔滨工业大学 计算硅锗超晶格材料界面热阻的方法
US20210269318A1 (en) * 2018-06-20 2021-09-02 University Of Houston System Unusual High Thermal Conductivity in Boron Arsenide Bulk Crystals
CN113987841A (zh) * 2021-12-24 2022-01-28 苏州浪潮智能科技有限公司 一种求解界面处声子热输运的方法和存储介质

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107942375B (zh) * 2017-11-17 2019-04-30 河海大学 一种基于声波方程的非线性优化隐式时空域有限差分数值模拟方法
CN110275733B (zh) * 2019-06-27 2022-11-22 上海交通大学 基于有限体积法求解声子玻尔兹曼方程的gpu并行加速方法
CN111986733B (zh) * 2020-07-16 2023-08-11 西安理工大学 一种纳米级水泥导热性能增强相材料的预选方法

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070230135A1 (en) * 2006-03-31 2007-10-04 International Business Machines Corporation Heat transfer control structures using thermal phonon spectral overlap
CN101760183A (zh) * 2009-12-30 2010-06-30 哈尔滨工业大学 计算硅锗超晶格材料界面热阻的方法
US20210269318A1 (en) * 2018-06-20 2021-09-02 University Of Houston System Unusual High Thermal Conductivity in Boron Arsenide Bulk Crystals
CN113987841A (zh) * 2021-12-24 2022-01-28 苏州浪潮智能科技有限公司 一种求解界面处声子热输运的方法和存储介质

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
FENG DAI-LI, FENG YAN-HUI, SHI JUN: "Lattice Boltzamn model of phonon heat conduction in mesoporous composite material", ACTA PHYSICA SINICA, vol. 65, no. 24, 1 January 2016 (2016-01-01), pages 244401, XP093074180, ISSN: 1000-3290, DOI: 10.7498/aps.65.244401 *
JEAN-PHILIPPE PERAUD; NICOLAS HADJICONSTANTINOU: "Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations", ARXIV.ORG, CORNELL UNIVERSITY LIBRARY, 201 OLIN LIBRARY CORNELL UNIVERSITY ITHACA, NY 14853, 18 September 2011 (2011-09-18), 201 Olin Library Cornell University Ithaca, NY 14853 , XP080528340, DOI: 10.1103/PhysRevB.84.205331 *
PERAUD, JEAN-PHILIPPE M. ET AL.: "Adjoint-based deviational Monte Carlo methods for phonon transport calculations", PHYSICAL REVIEW B, 31 December 2015 (2015-12-31), XP093074178 *
RAN XIN, GUO YANG-YU; WANG MO-RAN: "Monte Carlo Simulation of Interfacial Phonon Transport Through Bilayer Thin Film", JOURNAL OF ENGINEERING THERMOPHYSICS / ZHONGGUO GONGCHENG REWULI XUEHUI, KEXUE CHUBANSHE, BEIJING, vol. 38, no. 4, 30 April 2017 (2017-04-30), Beijing , pages 841 - 846, XP093074174, ISSN: 0253-231X *

Also Published As

Publication number Publication date
CN113987841A (zh) 2022-01-28
CN113987841B (zh) 2022-04-19

Similar Documents

Publication Publication Date Title
Bui-Thanh et al. Model reduction for large-scale systems with high-dimensional parametric input space
Wang et al. A meshless local radial basis function method for two-dimensional incompressible Navier-Stokes equations
WO2023115815A1 (fr) Procédé de résolution de transport thermique de phonons au niveau d'une interface, et support d'enregistrement
DeGroot et al. Numerical results for the effective flow and thermal properties of idealized graphite foam
US20220058315A1 (en) Simulating heat flux in additive manufacturing
Sun et al. An Improved Interpolating Element‐Free Galerkin Method Based on Nonsingular Weight Functions
Abdulle et al. An offline–online homogenization strategy to solve quasilinear two‐scale problems at the cost of one‐scale problems
Ni et al. Phonon transport modeling using Boltzmann transport equation with anisotropic relaxation times
Jin et al. Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids
Mehdi Keshtkar et al. Numerical simulation of radiative-conductive heat transfer in an enclosure with an isotherm obstacle
Zhao et al. An efficient transient analysis method for linear time-varying structures based on multi-level substructuring method
Wang et al. Solving of Two‐Dimensional Unsteady Inverse Heat Conduction Problems Based on Boundary Element Method and Sequential Function Specification Method
Elizarova et al. Quasi-gasdynamic model and numerical algorithm for describing mixtures of different fluids
Tensuda et al. Multi-dimensional validation of a maximum-entropy-based interpolative moment closure
Ravash et al. Three-dimensional phase-field simulation of microstructural evolution in three-phase materials with different diffusivities
Droniou et al. A uniformly converging scheme for fractal conservation laws
SULAIMAN et al. NUMERICAL SOLUTIONS OF NONLINEAR SECOND-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS USING HALF-SWEEP SOR WITH NEWTON METHOD.
Frank et al. Identification of temperature-dependent boundary conditions using MOR
Al Jahdali et al. Optimized explicit Runge-Kutta schemes for entropy stable discontinuous collocated methods applied to the euler and navier–stokes equations
Shterev Iterative process acceleration of calculation of unsteady, viscous, compressible, and heat‐conductive gas flows
Gelfgat On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess
Kamyshin et al. Algorithm for solving the Navier–Stokes equations for the modeling of creeping flows
Mori Peierls barrier of screw dislocation in bcc iron at finite temperature
Ingraham et al. External verification analysis: A code-independent verification technique for unsteady PDE codes
Hosseinizadeh et al. Numerical study of high gradient thermobuoyant flow in a tilted cavity using a novel non-boussinesq algorithm

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 22909150

Country of ref document: EP

Kind code of ref document: A1