A contact thermal resistance measurement method considering interface roughness distribution

Abstract

The present invention discloses a contact thermal resistance measurement method that takes into account the interface roughness distribution, and belongs to the field of thin film deposition technology. The method includes obtaining the topographical structure data of the upper surface of the lower film, and constructing the surface distribution function of the lower film based on the topographical structure data of the upper surface of the lower film; after the upper film is deposited, obtaining the topographical structure data of the upper surface of the upper film, and constructing the surface distribution function of the upper film based on the topographical structure data of the upper surface of the upper film; calculating the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film; rotating the three-dimensional graph of the upper film along the central axis according to a set angle, and calculating the void ratio after each rotation; constructing finite element models with different void ratios based on the initial void ratio and the void ratio after each rotation, and measuring the contact thermal resistance under different void ratios. The present invention takes into account the influence of the interface roughness distribution on the contact thermal resistance and obtains the contact thermal resistance under different void ratios.

Description

Technical Field

[0001] The invention belongs to the technical field of thin film deposition, and in particular relates to a contact thermal resistance measurement method taking interface roughness distribution into consideration. Background Art

[0002] Deposition processes play a crucial role in manufacturing processes such as semiconductor packaging. Deposition processes are primarily used to form thin films on or within chip surfaces. These films can be insulating, conductive, or semiconducting layers. The thermal characteristics of the deposition process significantly impact film quality, as well as product performance and reliability. Therefore, establishing a complete and accurate thermal model of the deposition process requires considering the impact of contact thermal resistance.

[0003] However, existing methods for measuring interfacial contact thermal resistance are based on idealized models and fail to consider the impact of interface roughness distribution. Interface roughness can create pores of varying sizes between interfaces, which can affect the accuracy of interfacial contact thermal resistance measurements. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a contact thermal resistance measurement method that takes into account the interface roughness distribution. The influence of the interface roughness distribution on the contact thermal resistance is taken into account to obtain the contact thermal resistance under different void proportions.

[0005] The present invention provides the following technical solutions:

[0006] In a first aspect, a contact thermal resistance measurement method taking into account the interface roughness distribution is provided, comprising: obtaining morphological structure data of the upper surface of a lower film, and constructing a surface distribution function of the lower film based on the morphological structure data of the upper surface of the lower film; after the upper film is deposited, obtaining morphological structure data of the upper surface of the upper film, and constructing a surface distribution function of the upper film based on the morphological structure data of the upper surface of the upper film; calculating the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film; rotating the three-dimensional image of the upper film along the central axis at a set angle in a three-dimensional model space based on the morphological structure data of the upper surface of the lower film and the upper surface of the upper film, and calculating the void ratio after each rotation; constructing finite element models with different void ratios based on the initial void ratio and the void ratio after each rotation, and measuring the contact thermal resistance under different void ratios through the finite element model.

[0007] As an optional technical solution of the present invention, the topographic structure data is represented as a three-dimensional matrix , where x0 and y0 represent the horizontal and vertical coordinate values ​​of any point on the film surface, respectively, and z0 represents the height value of the point.

[0008] As an optional technical solution of the present invention, the step of obtaining the topographical structure data of the upper surface of the upper film and constructing the surface distribution function of the upper film according to the topographical structure data of the upper surface of the upper film includes:

[0009] Ideally, the roughness distribution of the lower surface of the upper film corresponds to the roughness distribution of its upper surface. The distribution function constructed using the topographical structure data of the upper surface of the upper film is used as the distribution function of the lower surface of the upper film to obtain the surface distribution function of the upper film.

[0010] As an optional technical solution of the present invention, the surface distribution of the lower film or the upper film has self-similarity, and the surface distribution function of the lower film or the surface distribution function of the upper film , expressed as:

[0011] ;

[0012] in, represents the amplitude coefficient, represents the frequency coefficient, and n represents the number of iterations.

[0013] As an optional technical solution of the present invention, the surface distribution of the lower film or the upper film does not have self-similarity, and the surface distribution function of the lower film or the surface distribution function of the upper film , expressed as:

[0014] ;

[0015] in, represents independent and identically distributed Gaussian random variables with mean 0 and variance , i represents the i-th Gaussian random variable, and m represents the total number of Gaussian random variables.

[0016] As an optional technical solution of the present invention, the calculation of the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film includes:

[0017] constructing a simplified film interface contact model based on the surface distribution function of the lower film and the surface distribution function of the upper film, and calculating the volume of the simplified film interface contact model;

[0018] Calculate the initial interface gap height , expressed as:

[0019] ;

[0020] in, represents the surface distribution function of the lower film, represents the surface distribution function of the upper film;

[0021] If exists , then let the position Initial interface gap height at ;

[0022] Calculate the initial interfacial gap volume , expressed as:

[0023] ;

[0024] The initial void ratio , expressed as:

[0025] ;

[0026] Where V represents the volume of the simplified model of the thin film interface contact.

[0027] As an optional technical solution of the present invention, the initial interface gap height , also expressed as:

[0028] ;

[0029] ;

[0030] ;

[0031] in, Indicates the maximum height of the lower film surface, Indicates the minimum height of the lower film surface, Indicates the maximum height of the upper film surface, Indicates the minimum height of the upper film surface.

[0032] As an optional technical solution of the present invention, the three-dimensional image of the upper film is rotated along the central axis at a set angle, and the void ratio after each rotation is calculated, including: each time the three-dimensional image of the upper film is rotated by a set angle, the coordinates of each position point on the three-dimensional image of the upper film undergo quantitative changes, the new coordinates of each position point are brought into the surface distribution function of the upper film to recalculate the interface gap height, and the void ratio is recalculated based on the new interface gap height, until the rotation is 360°.

[0033] As an optional technical solution of the present invention, the contact thermal resistance , expressed as:

[0034] ;

[0035] in, represents the temperature difference between the lower film and the upper film, q represents the heat flux per unit area, Represent the temperatures of the lower and upper films, respectively.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] The contact thermal resistance measurement method considering the interface roughness distribution provided by the present invention takes into account the influence of the roughness distribution of the upper and lower film interfaces on the contact thermal resistance measurement. By rotating the upper film, the relative positions of the upper and lower films are changed to change the void ratio, and then the contact thermal resistance under different void ratios is measured, which is closer to the actual situation and provides a theoretical basis for analyzing the contact thermal resistance of the interface during the thin film deposition process. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flow chart of a contact thermal resistance measurement method considering interface roughness distribution in an embodiment of the present invention;

[0039] Figure 2 Schematic diagram of the three-dimensional topography of the upper surface of the lower film in an embodiment of the present invention.

[0040] Figure 3 Schematic diagram of thin film interface contact in an embodiment of the present invention;

[0041] Figure 4 Schematic diagram of a simplified film interface contact model and models with different void ratios in an embodiment of the present invention;

[0042] Figure 5 Schematic diagram of the relationship between the void ratio and the contact thermal resistance in an embodiment of the present invention.

[0043] Marked in the figure: 1, upper film; 2, interface gap; 3, lower film. DETAILED DESCRIPTION

[0044] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0045] In manufacturing processes such as semiconductor packaging, two or more thin films are deposited on the chip surface. Ideally, this method assumes the roughness distribution of the upper and lower surfaces of the upper film is consistent. However, when using this method to measure the contact thermal resistance between two layers of deposited films, the significant difference in roughness distribution between the upper and lower surfaces of the upper film can increase measurement error. Therefore, this method is primarily suitable for depositing two thin films.

[0046] Example 1

[0047] This embodiment provides a contact thermal resistance measurement method that takes into account the interface roughness distribution. Figure 1 As shown, the following steps are included:

[0048] Step 1: Acquire the topographical structure data of the upper surface of the lower film 3 , and construct the surface distribution function of the lower film according to the topographical structure data of the upper surface of the lower film 3 .

[0049] Specifically, after the lower film 3 is deposited, the nanoscale 3D optical interferometry system is used to measure the topographical structure data of the upper surface of the lower film 3 and record the surface roughness distribution. The topographical structure data is represented by a three-dimensional matrix , where x0 and y0 represent the horizontal and vertical coordinate values ​​of any point on the film surface, respectively, and z0 represents the height value of the point.

[0050] Step 2: After the upper film 1 is deposited, the topographical structure data of the upper surface of the upper film 1 is obtained, and the surface distribution function of the upper film is constructed according to the topographical structure data of the upper surface of the upper film.

[0051] Specifically, an upper film 1 is deposited on a lower film 3, and the topographical structure data of the upper surface of the upper film 1 is measured. Ideally, the roughness distribution of the lower surface of the upper film corresponds to the roughness distribution of its upper surface. A distribution function constructed using the topographical structure data of the upper film's upper surface is used as the distribution function of the lower surface of the upper film to obtain the upper film surface distribution function. That is, the lower surface condition and distribution function can be obtained from the upper surface roughness and distribution function.

[0052] In step 1 and step 2, different distribution functions need to be used according to different conditions of the film surface. The details are as follows:

[0053] (1) The surface distribution of the lower film or the upper film has self-similarity, and the surface distribution function of the lower film or the surface distribution function of the upper film , expressed as:

[0054] ;

[0055] in, represents the amplitude coefficient, which decreases with the increase of n to ensure the self-similarity and convergence of the fractal surface. represents the frequency coefficient, which controls the change in the characteristic dimensions of the film surface. n represents the number of iterations used to construct the fractal surface. In actual calculations, as n increases, the contribution of each term to the total surface height gradually decreases. Iterations are stopped when the surface height change caused by the iterations is no longer significant.

[0056] (2) The surface distribution of the lower film or the upper film does not have self-similarity, and the surface distribution function of the lower film or the surface distribution function of the upper film , expressed as:

[0057] ;

[0058] in, represents independent and identically distributed Gaussian random variables with mean 0 and variance , i represents the i-th Gaussian random variable, and m represents the total number of Gaussian random variables.

[0059] Step 3: Calculate the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film. Specifically including:

[0060] 3.1. Construct a simplified film interface contact model based on the surface distribution function of the lower film and the surface distribution function of the upper film, and calculate the volume of the simplified film interface contact model.

[0061] 3.2. Calculate the initial interface gap height , this embodiment provides two calculation methods.

[0062] (1) Initial interface gap height Expressed as:

[0063] ;

[0064] in, represents the surface distribution function of the lower film, represents the surface distribution function of the upper film.

[0065] If exists , then let the position Initial interface gap height at .

[0066] (2) The initial interface gap height , also expressed as:

[0067] ;

[0068] ;

[0069] ;

[0070] in, Indicates the maximum height of the lower film surface, Indicates the minimum height of the lower film surface, Indicates the maximum height of the upper film surface, Indicates the minimum height of the upper film surface.

[0071] 3.3. Calculation of initial interface gap volume , expressed as:

[0072] ;

[0073] The initial void ratio , expressed as:

[0074] ;

[0075] Where V represents the volume of the simplified model of the thin film interface contact.

[0076] Step 4: Based on the topographical structure data of the upper surface of the lower film and the upper surface of the upper film, in the three-dimensional model space, rotate the three-dimensional image of the upper film along the central axis at a set angle, and calculate the void ratio after each rotation.

[0077] Specifically, each time the three-dimensional image of the upper film is rotated by a set angle, the coordinates of each position point on the three-dimensional image of the upper film change quantitatively. The new coordinates of each position point are brought into the surface distribution function of the upper film to recalculate the interface gap height, and the void ratio is recalculated based on the new interface gap height until the rotation is 360°.

[0078] Step 5: Based on the initial void ratio and the void ratio after each rotation, construct finite element models with different void ratios, and measure the contact thermal resistance under different void ratios through the finite element model.

[0079] The contact thermal resistance , expressed as:

[0080] ;

[0081] in, represents the temperature difference between the lower film and the upper film, q represents the heat flux per unit area, Represent the temperatures of the lower and upper films, respectively.

[0082] Example 2

[0083] Based on Example 1, this example provides an application of the method described in Example 1.

[0084] Step 1: In this embodiment, the surfaces of the upper film 1 and the lower film 3 are both self-similar. The amplitude attenuation coefficient a of the upper surface of the lower film 3 is 0.4, the frequency growth coefficient b is 1.8, and the number of iterations is n=10. The three-dimensional morphology of the upper surface of the lower film is as follows: Figure 2The surface amplitude attenuation coefficient of the upper film 1 is a=0.5, the frequency growth coefficient is b=2, and the number of iterations is n=10. The interface contact of the two films is shown as follows: Figure 3 shown.

[0085] The surface distribution function of the lower film is expressed as:

[0086] ;

[0087] The surface distribution function of the upper film is expressed as:

[0088] .

[0089] Step 2: Calculate the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film. The details are as follows:

[0090] 2.1. Construct a simplified model of film interface contact based on the surface distribution function of the lower film and the upper film. Figure 4 As shown, the overall shape of the simplified film interface contact model is circular, the cross-sectional diameter is 35 μm, and the thickness of the upper and lower film layers is 0.8 μm.

[0091] 2.2, use The volume of the interface gap in the initial state was calculated by integration, and the initial void ratio was finally obtained to be 23.76%.

[0092] Step 3: Calculate the change in void ratio by adjusting the relative angle between the upper and lower films.

[0093] The three-dimensional image of the upper film was rotated along the central axis by 20° each time, and the size of the void ratio after rotation was measured. Then, based on the 18 sets of measured data, it was summarized that the void ratio range was 15.74%-64.53%.

[0094] Step 4: Select three points from the range of void ratio measured in step 3, namely 20%, 33% and 50%, respectively, establish finite element models for each point, and measure the corresponding contact thermal resistance.

[0095] like Figure 4 As shown, the four figures above represent a simplified model of the film interface contact and finite element models with different void ratios. To approximate the distribution of the interfacial gap, three evenly spaced square holes are set. At the same time, the square holes are adjusted to different sizes to simulate different void ratios. The four figures below show the contact thermal resistance measurement process. The left side shows the heat source and cold source temperatures set to 398K and 298K, respectively. The three figures on the right are heat distribution diagrams during the contact thermal resistance measurement of the finite element models with three different void ratios.

[0096] like Figure 5 As shown, by measuring the contact thermal resistance of the finite element model with different void ratios, the relationship between the void ratio and the contact thermal resistance is obtained, and a related curve is drawn. In this embodiment, the relationship between the contact thermal resistance and the void ratio of three different material film interfaces is tested, namely the tungsten (W) and silicon dioxide (SiO2) interface, the tungsten (W) and silicon (Si) interface, and the tungsten (W) and copper (Cu) interface. Among the three interfaces, it can be clearly seen that the void ratio has the greatest impact on the interface contact thermal resistance of tungsten (W) and silicon dioxide (SiO2), and has little impact on the contact thermal resistance of the other two interfaces. But overall, the void ratio is positively correlated with the contact thermal resistance, and the degree of influence is related to the type of interface material.

[0097] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0099] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0101] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A contact thermal resistance measurement method considering interface roughness distribution, characterized in that: include: Acquiring topographical structure data of the upper surface of the lower film, and constructing a surface distribution function of the lower film according to the topographical structure data of the upper surface of the lower film; After the upper film is deposited, topographical structure data of the upper surface of the upper film is obtained, and a surface distribution function of the upper film is constructed according to the topographical structure data of the upper surface of the upper film; Calculating the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film; Based on the topographical structural data of the upper surface of the lower film and the upper surface of the upper film, in the three-dimensional model space, the three-dimensional image of the upper film is rotated along the central axis according to a set angle, and the void ratio after each rotation is calculated; According to the initial void ratio and the void ratio after each rotation, finite element models with different void ratios are constructed, and the contact thermal resistance under different void ratios is measured using the finite element model.

2. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The topographic structure data is represented as a three-dimensional matrix , where x0 and y0 represent the horizontal and vertical coordinate values ​​of any point on the film surface, respectively, and z0 represents the height value of the point.

3. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The obtaining of the topographical structure data of the upper surface of the upper film and constructing the surface distribution function of the upper film according to the topographical structure data of the upper surface of the upper film includes: Ideally, the roughness distribution of the lower surface of the upper film corresponds to the roughness distribution of its upper surface. The distribution function constructed using the topographical structure data of the upper surface of the upper film is used as the distribution function of the lower surface of the upper film to obtain the surface distribution function of the upper film.

4. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The surface distribution of the lower film or the upper film has self-similarity, and the surface distribution function of the lower film or the surface distribution function of the upper film , expressed as: ； in, represents the amplitude coefficient, represents the frequency coefficient, and n represents the number of iterations.

5. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The surface distribution of the lower film or the upper film does not have self-similarity, and the surface distribution function of the lower film or the surface distribution function of the upper film , expressed as: ； in, represents independent and identically distributed Gaussian random variables with mean 0 and variance , i represents the i-th Gaussian random variable, and m represents the total number of Gaussian random variables.

6. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The calculating of the initial void ratio based on the surface distribution function of the lower film and the surface distribution function of the upper film includes: constructing a simplified film interface contact model based on the surface distribution function of the lower film and the surface distribution function of the upper film, and calculating the volume of the simplified film interface contact model; Calculate the initial interface gap height , expressed as: ； in, represents the surface distribution function of the lower film, represents the surface distribution function of the upper film; If exists , then let the position Initial interface gap height at ; Calculate the initial interfacial gap volume , expressed as: ； The initial void ratio , expressed as: ； Where V represents the volume of the simplified model of the thin film interface contact.

7. The contact thermal resistance measurement method considering interface roughness distribution according to claim 6, characterized in that: The initial interface gap height , also expressed as: ； ； ； in, Indicates the maximum height of the lower film surface, Indicates the minimum height of the lower film surface, Indicates the maximum height of the upper film surface, Indicates the minimum height of the upper film surface.

8. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The step of rotating the upper film three-dimensional image along the central axis at a set angle and calculating the void ratio after each rotation includes: Each time the three-dimensional image of the upper film is rotated by a set angle, the coordinates of each position point on the three-dimensional image of the upper film change quantitatively. The new coordinates of each position point are brought into the surface distribution function of the upper film to recalculate the interface gap height, and the void ratio is recalculated based on the new interface gap height until the rotation is 360°.

9. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The contact thermal resistance , expressed as: ； in, represents the temperature difference between the lower film and the upper film, q represents the heat flux per unit area, Represent the temperatures of the lower and upper films, respectively.

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