A micro-device electro-thermal coupling modeling analysis method involving thermal boundary conditions

Abstract

The application provides a micro-device electro-thermal coupling modeling analysis method related to thermal boundary conditions, which comprises the following steps: constructing a geometric model of a micro-device according to the structure and packaging of the micro-device, then adding various parameters to the geometric model to obtain an equivalent model representing the overall structure, input and output relationship of the micro-device; and constraining the equivalent model through equivalent thermal boundary conditions to simulate the influence of thermal effects and electro-thermal coupling on the device under a real environment, so as to obtain an electro-thermal coupling model with a predicted transient thermal response. The application can more accurately evaluate the heat dissipation of the micro-device under a real environment and more accurately predict the working state and thermal stability of the micro-device by modeling the equivalent model representing the overall structure, input and output relationship of the micro-device and the packaging equivalent thermal resistance, combining the two models to obtain a thermal-electric coupling model more in line with the actual heat exchange of the micro-device, and then adding an electric signal to test and analyze the thermal-electric coupling model.

Description

Technical Field

[0001] This invention belongs to the field of microdevice design technology, specifically relating to a microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions. Background Technology

[0002] The thermal effects of microdevices significantly impact their performance and reliability. For example, the electrical characteristics of transistors, diodes, and field-effect transistors change with temperature. Therefore, studying and optimizing the thermal effects of microdevices is crucial. Microdevices possess unique properties at the microscale; their heat and electrical conduction mechanisms differ greatly from those at the macroscale, and the distribution of heat and current may exhibit nonlinearity and non-uniformity. Therefore, electrothermal coupling modeling of microdevices must consider both the internal temperature distribution and heat exchange with the external environment.

[0003] Modeling methods based on the SIPCE model can parametrically describe the electrical characteristics of devices, but they lack underlying physical analysis due to their behavior and data fitting approach. Finite element method (FEM) numerical calculations, on the other hand, decompose the device into many small units, perform numerical calculations on each unit, and ultimately obtain the electrothermal distribution of the entire device. This method is currently a commonly used electrothermal coupling modeling approach for microdevices.

[0004] Currently, there are two main types of modeling and simulation methods. The first type is the electro-thermal single-coupling method, which calculates the heat power generated by the device through electrical signals, then models the obtained heat power as a heat source, and finally calculates heat diffusion. This method lacks calculations regarding the impact of temperature distribution on electrical heat generation. The second type is the electro-thermal two-coupling method, which involves the interaction of temperature distribution, electric field intensity distribution, and current density distribution in the device model, and performs coupled calculations. Currently, the second type of electro-thermal two-coupling method typically sets the model substrate as an isothermal boundary while other surfaces are adiabatic, i.e., ideal heat sink boundary conditions. However, with the advancement of packaging technologies, such as 3D packaging and double-sided mounting, microdevices have more options for heat dissipation, and heat dissipation performance has improved. This makes setting the microdevice substrate as the sole heat dissipation boundary no longer applicable. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions, including:

[0007] S100: Obtain the physical property parameters of the microdevice and construct the geometric model of the microdevice based on the physical property parameters;

[0008] S200: Input the geometric model into the simulation software to simultaneously solve the semiconductor Poisson equation, the current continuity equation, and the thermodynamic model in the simulation software to obtain an equivalent model that describes the overall structure, input and output relationship of the microdevice.

[0009] S300 determines the equivalent thermal boundary conditions of the microdevice package based on the microdevice's packaging configuration.

[0010] S400, the equivalent thermal boundary conditions are used to constrain the equivalent model to obtain the electrothermal coupling model;

[0011] The S500 analyzes and tests the internal peak temperature of the microdevice over time and the transient temperature distribution by adding an electrical signal to the electrothermal coupling model.

[0012] This invention provides a method for modeling and analyzing the electrothermal coupling of microdevices involving thermal boundary conditions. It involves constructing a geometric model of the microdevice based on its structure and packaging, then adding parameters to this geometric model to obtain an equivalent model that describes the overall structure, input, and output relationships of the microdevice. The equivalent model is constrained by equivalent thermal boundary conditions to simulate the effects of thermal effects and electrothermal coupling on the device under real-world conditions, thereby obtaining an electrothermal coupling model capable of predicting transient thermal responses. This invention, by modeling the equivalent model describing the overall structure, input, and output relationships of the microdevice and modeling the equivalent thermal resistance of the packaging, and combining these two models, yields a more realistic thermoelectric coupling model of the microdevice's heat exchange. Adding electrical signals to test and analyze the thermoelectric coupling model allows for a more accurate assessment of the microdevice's heat dissipation under real-world conditions and a more precise prediction of the microdevice's operating state and thermal stability.

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions provided by the present invention;

[0015] Figure 2 This is a schematic diagram of the device material structure provided by the present invention;

[0016] Figure 3 This is a schematic diagram of the heat dissipation path provided by the present invention;

[0017] Figure 4 This is the curve showing the change of the internal peak temperature of the device over time, provided by the present invention.

[0018] Figure 5 This is a schematic diagram of the temperature distribution of the device provided by the present invention;

[0019] Figure 6 This is a schematic diagram of the discrete meshing of the geometric model provided by the present invention;

[0020] Figures 7a-7c This is a schematic diagram of the transient temperature distribution diagram provided by the present invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0022] like Figure 1 As shown, this invention provides a microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions, including:

[0023] S100: Obtain the physical property parameters of the microdevice and construct the geometric model of the microdevice based on the physical property parameters;

[0024] This invention uses a schematic diagram of the material structure of a high electron mobility transistor (HEMT) as an example, as shown in the attached diagram. Figure 2 As shown.

[0025] The heat dissipation path determination method for the packaging structure proposed in this invention sets the thermal boundary thermal resistance range of the device, and its packaging heat dissipation path schematic diagram is attached. Figure 3 As shown, there are three cases:

[0026] exist Figure 3 As shown in Figure a, the device is a single-sided mount device with a metal bonding structure. The upper surface of the device is filled with gas, and the heat of the device is mainly dissipated through the bottom contact.

[0027] exist Figure 3 As shown in Figure b, in single-sided mounting with encapsulation material, the upper surface of the device also has thermal conductivity due to the encapsulation material.

[0028] exist Figure 3 As shown in Figure c, the double-sided surface mount copper interconnect structure provides good thermal conductivity on both the upper and lower surfaces of the device.

[0029] S200: Input the geometric model into Sentaurus TCAD software to simultaneously solve the semiconductor Poisson equation, the current continuity equation, and the thermodynamic model in Sentaurus TCAD software to obtain an equivalent model that describes the overall structure, input and output relationship of the microdevice.

[0030] S300 determines the equivalent thermal boundary conditions of the microdevice package based on the microdevice's packaging configuration.

[0031] S400, the equivalent thermal boundary conditions are used to constrain the equivalent model to obtain the electrothermal coupling model;

[0032] The S500 analyzes and tests the internal peak temperature of the microdevice over time and the transient temperature distribution by adding an electrical signal to the electrothermal coupling model.

[0033] The method for predicting the operating state and thermal stability of microdevices proposed in this invention mainly obtains the transient electrothermal response and temperature distribution of the device by adding an external electrical signal, and then analyzes the device's operating state and thermal stability. Specifically, the transient electrothermal response of the device includes the time-varying curves of the voltage and current signals at the device's electrode ports, and the time-varying curve of the peak internal temperature of the device. Through these time-varying parameter curves, it is possible to analyze when the device reaches the melting point of the material and suffers burn-out damage. The transient electrothermal response of the device can be represented by the time-varying curve of the peak internal temperature of the device, as shown in the attached figure. Figure 4 As shown. (Through) Figure 4 This allows analysis of the device's damage thermal response under different thermal boundary conditions. The device temperature distribution, specifically the temperature distribution at any given moment in the transient simulation, is shown in the attached figure. Figure 5 As shown. Through this temperature distribution Figure 5 It can analyze the location of high-temperature regions in devices.

[0034] The accompanying drawings of this invention only show the modeling objects that can be used as HEMT devices. This invention can replace different device types to perform electrothermal coupling modeling and analysis of devices involving thermal boundary conditions, thereby achieving the same inventive purpose, and all of these fall within the scope of protection of this invention.

[0035] This invention provides a method for modeling and analyzing the electrothermal coupling of microdevices involving thermal boundary conditions. It involves constructing a geometric model of the microdevice based on its structure and packaging, then adding parameters to this geometric model to obtain an equivalent model that describes the overall structure, input, and output relationships of the microdevice. The equivalent model is constrained by equivalent thermal boundary conditions to simulate the effects of thermal effects and electrothermal coupling on the device under real-world conditions, thereby obtaining an electrothermal coupling model capable of predicting transient thermal responses. This invention, by modeling the equivalent model describing the overall structure, input, and output relationships of the microdevice and modeling the equivalent thermal resistance of the packaging, and combining these two models, yields a more realistic thermoelectric coupling model of the microdevice's heat exchange. Adding electrical signals to test and analyze the thermoelectric coupling model allows for a more accurate assessment of the microdevice's heat dissipation under real-world conditions and a more precise prediction of the microdevice's operating state and thermal stability.

[0036] In an optional embodiment of the present invention, S100 includes:

[0037] S110, obtain the layer structure, material distribution, general material parameters, and packaging heat dissipation structure of the microdevice;

[0038] S120 constructs a geometric model of a microdevice based on the layer structure, material distribution, general material parameters, and packaging heat dissipation structure.

[0039] In an optional embodiment of the present invention, S200 includes:

[0040] S210, The geometric model is discretized into a mesh according to the operating conditions of the microdevice. This invention discretizes the geometric model into a mesh as follows: Figure 6 As shown.

[0041] S220, in Sentaurus TCAD software, select the semiconductor Poisson equation, the current continuity equation and the thermodynamic model respectively;

[0042] The semiconductor Poisson equation in S220 of this invention describes the relationship between the carrier distribution and the potential inside the semiconductor, and is expressed as: ..(1);

[0044] Where ε is the dielectric constant of the material, q is the electric potential, p is the hole concentration, n is the electron concentration, and N is the net doping concentration of the material.

[0045] The current density equation in S220 of this invention, used to describe the current flow in relation to thermal effects, is expressed as follows:

[0046]

[0047] Where, μ n It is the electron mobility, μ p It is the hole mobility, φ n φ p Both are quasi-Fermi potentials of the materials. It is the thermal contribution of electrons. It is the heat contribution item of the cavity;

[0048] The thermodynamic model in S220 of this invention, used to describe the relationship between lattice temperature and heat inside a semiconductor, is expressed as follows:

[0049]

[0050] Among them, c L κ is the lattice heat capacity of the material, k is the thermal conductivity of the material, and E is the Boltzmann constant. C and E V These are the conduction band and valence band energy levels of the material, R. n ' is the electron recombination coefficient, Rp ' is the recombination coefficient of holes, P n ' is the thermal power generated by electrons, P p 'It is the heat power generated by the hole.'

[0051] S230, define the variable parameters of the equivalent model to obtain the equivalent model that describes the overall structure, input and output relationship of the microdevice.

[0052] In an optional embodiment of the present invention, S300 includes:

[0053] S310 sets the boundary temperature of the microdevice to the ambient temperature;

[0054] S320 sets the thermal boundary range of the device according to the packaging structure of the microdevice;

[0055] S330, based on the physical properties of the microdevice, ambient temperature, and thermal boundary range, obtains the equivalent thermal boundary conditions;

[0056] The equivalent thermal boundary conditions include: the device thermal boundary range, the thermal resistance per unit area of ​​the thermal boundary, and the ambient temperature.

[0057] The thermal resistance per unit area of ​​the thermal boundary is expressed as:

[0058] r T =R T ·A(4);

[0059] Where, r T Thermal resistance per unit surface area of ​​the thermal contact surface of the device, in cm. 2 ·K / W, R T The junction resistance to ambient temperature is expressed in K / W, and A is the total thermal contact area of ​​the device, expressed in cm². 2 .

[0060] In an optional embodiment of the present invention, S500 includes:

[0061] S510: Based on the discrete mesh generation results of S210, establish the boundary conditions for a single element.

[0062] The boundary conditions of a single unit include a set of numerical equations for potential boundary, electron-hole concentration and temperature boundary.

[0063] See Figure 7a Taking a one-dimensional unit as an example, the boundary conditions of a single unit are established according to equations (1), (2), and (3), including a set of numerical equations for potential boundary, electron-hole concentration and temperature boundary.

[0064]

[0065] Where N is the net doping concentration, n i Where E is the intrinsic carrier concentration of the material, T is the temperature, and E is the intrinsic carrier concentration. T This refers to the net heat capacity per unit.

[0066] The description of the set of cells after meshing is as follows Figure 7b As shown, in Figure 7b In the case of k = (1, 3, ..., L-1).

[0067] S520, based on the boundary conditions and equivalent thermal boundary conditions of each element, performs finite element difference calculations on the semiconductor Poisson equation, current continuity equation and thermodynamic model under the input signal, and obtains a set of difference approximation equations related to the variables.

[0068] This invention differentiates the finite differences of equations (1), (2), and (3) into variables. A system of difference approximation equations related to n, p, and T:

[0069]

[0070] This invention is based on the numerical calculation method of finite element method, which can decompose the device into many small elements, perform numerical calculation on each element, and finally obtain the electrothermal distribution of the entire device.

[0071] S530, the difference approximation equations of the element are set into a Jacobi numerical matrix, and the nodal parameter values ​​of all elements are obtained by solving the synthetic equations through the Newton-Raphson iteration method.

[0072] This invention sets the difference approximation equations of the unit into a Jacobi numerical matrix, and solves the comprehensive equation system Ax=b by Newton's iteration method.

[0073]

[0074] See the solution process of Newton's iteration method. Figure 7c The iterative convergence criterion is as follows:

[0075] Convergence Criterion 1: RHS error, i.e., the residual term of the equation.

[0076]

[0077] Convergence Criterion 2: Relative error, the proportion of error updates.

[0078]

[0079] Where x0 is the result of the previous iteration; Δx is the update amount.

[0080] The invention finally obtains the node parameter values ​​of all elements, for example...

[0081] S540 assembles the node parameter values ​​of all units into a transient temperature distribution map, and assembles the trend of the highest temperature value over time into a peak temperature over time curve.

[0082] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0083] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple components.

[0084] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for electrothermal coupling modeling and analysis of microdevices involving thermal boundary conditions, characterized in that, include: S100: Obtain the physical property parameters of the microdevice and construct the geometric model of the microdevice based on the physical property parameters; S200, The geometric model is input into the simulation software to simultaneously solve the semiconductor Poisson equation, the current continuity equation and the thermodynamic model in the simulation software to obtain an equivalent model that describes the overall structure, input and output relationship of the microdevice. S300 determines the equivalent thermal boundary conditions of the microdevice package based on the microdevice's packaging configuration. S400, constrain the equivalent thermal boundary conditions on the equivalent model to obtain an electrothermal coupling model; S500, by adding an electrical signal to the electrothermal coupling model for analysis and testing, obtains the trend of the internal peak temperature of the microdevice over time and the transient temperature distribution map.

2. The microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions according to claim 1, characterized in that, S100 includes: S110, obtain the layer structure, material distribution, general material parameters, and packaging heat dissipation structure of the microdevice; S120 constructs a geometric model of a microdevice based on the layer structure, material distribution, general material parameters, and packaging heat dissipation structure.

3. The microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions according to claim 1, characterized in that, S200 includes: S210, The geometric model is discretized into a mesh according to the working condition of the microdevice; S220, in Sentaurus TCAD software, select the semiconductor Poisson equation, the current continuity equation and the thermodynamic model respectively; S230, define the variable parameters of the equivalent model to obtain the equivalent model that describes the overall structure, input and output relationship of the microdevice.

4. The microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions according to claim 3, characterized in that, The semiconductor Poisson equation in S220 describes the relationship between the carrier distribution and electric potential inside a semiconductor, and is expressed as follows: Where ε is the dielectric constant of the material, q is the electric potential, p is the hole concentration, n is the electron concentration, and N is the net doping concentration of the material. The current density equation in S220, used to describe the current flow in the thermal effect, is expressed as: Where, μ n It is the electron mobility, μ p It is the hole mobility, φ n φ p Both are quasi-Fermi potentials of the materials. It is the thermal contribution of electrons. It is the heat contribution item of the cavity; The thermodynamic model in S220, used to describe the relationship between lattice temperature and heat within the semiconductor, is expressed as follows: Among them, c L κ is the lattice heat capacity of the material, k is the thermal conductivity of the material, and E is the Boltzmann constant. C and E V These are the conduction band and valence band energy levels of the material, R. n ' is the electron recombination coefficient, R p ' is the recombination coefficient of holes, P n ' is the thermal power generated by electrons, P p 'It is the heat power generated by the hole.' 5. The microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions according to claim 3, characterized in that, The S300 includes: S310 sets the boundary temperature of the microdevice to the ambient temperature; S320 sets the thermal boundary range of the device according to the packaging structure of the microdevice; S330, based on the physical property parameters of the microdevice, the ambient temperature, and the thermal boundary range, the equivalent thermal boundary conditions are obtained; The equivalent thermal boundary conditions include: the device thermal boundary range, the thermal resistance per unit area of ​​the thermal boundary, and the ambient temperature.

6. The microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions according to claim 5, characterized in that, The thermal resistance per unit area of ​​the thermal boundary is expressed as: r T =R T ·A (4); Where, r T Thermal resistance per unit surface area of ​​the thermal contact surface of the device, in cm. 2 ·K / W, R T The junction resistance to ambient temperature is expressed in K / W, and A is the total thermal contact area of ​​the device, expressed in cm². 2 .

7. The microdevice electrothermal coupling modeling and analysis method involving thermal boundary conditions according to claim 6, characterized in that, The S500 includes: S510: Based on the discrete mesh generation results of S210, establish the boundary conditions for a single element. The boundary conditions of a single unit include a set of numerical equations for potential boundary, electron-hole concentration and temperature boundary. S520, based on the boundary conditions of each unit and the equivalent thermal boundary conditions, finite element difference calculations are performed on the semiconductor Poisson equation, current continuity equation and thermodynamic model under the input signal to obtain a set of difference approximation equations related to the variables. S530, the difference approximation equations of the element are set into a Jacobi numerical matrix, and the nodal parameter values ​​of all elements are obtained by solving the synthetic equations through the Newton-Raphson iteration method. S540 uses the time-varying trends of all unit node parameter values ​​to create a transient temperature distribution map.

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