Contact thermal resistance measuring method considering interface roughness distribution

Abstract

The invention discloses a contact thermal resistance measuring method considering interface roughness distribution, and belongs to the technical field of thin film deposition. The method comprises the steps of obtaining morphology structure data of the upper surface of a lower-layer film, and constructing a lower-layer film surface distribution function according to the morphology structure data of the upper surface of the lower-layer film; after the upper-layer film is deposited, obtaining morphology structure data of the upper surface of the upper-layer film, and constructing an upper-layer film surface distribution function according to the morphology structure data of the upper surface of the upper-layer film; calculating an initial cavity ratio based on the lower-layer film surface distribution function and the upper-layer film surface distribution function; rotating the upper-layer film three-dimensional diagram along the central axis according to a set angle, and calculating a cavity proportion after each rotation; and according to the initial cavity ratio and the cavity ratio after each rotation, constructing finite element models of different cavity ratios, and measuring the contact thermal resistance under different cavity ratios. According to the method, the influence of interface roughness distribution on the contact thermal resistance is considered, and the contact thermal resistance under different cavity proportions is obtained.

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] In the manufacturing process of semiconductor packaging, the deposition process plays a vital role. The deposition process is mainly used to form thin films on the surface or inside the chip. These films can be insulating layers, conductive layers or semiconductor layers. The thermal characteristics of the deposition process have a significant impact on the quality of the film and the performance and reliability of the product. If you want to establish a complete and accurate thermal model of the deposition process, you have to consider the impact of contact thermal resistance.

[0003] However, the measurement of interface thermal contact resistance in the prior art is based on an idealized model, without considering the influence of interface roughness distribution. Interface roughness will cause pores of different sizes between interfaces, and the presence of these pores will affect the accuracy of interface thermal contact resistance measurement. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a contact thermal resistance measurement method that takes into account the interface roughness distribution, taking into account the influence of the interface roughness distribution on the contact thermal resistance, and obtaining 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 according to 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 according to the morphological structure data of the upper surface of the upper film; calculating an 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 surfaces of the lower film and the upper film, and calculating the void ratio after each rotation; constructing finite element models with different void ratios according to 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 morphological structure data is represented as a three-dimensional matrix , where x 0 ,y 0 Respectively represent the horizontal and vertical coordinate values ​​of any point on the film surface, z 0 Indicates the height value of the point.

[0008] As an optional technical solution of the present invention, the step of acquiring the topographic structure data of the upper surface of the upper film and constructing the surface distribution function of the upper film according to the topographic 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 morphological 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 interface 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 change quantitatively, and 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 according to 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 film and the upper film 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. This 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 It is a schematic diagram of the three-dimensional morphology of the upper surface of the lower film in an embodiment of the present invention.

[0040] Figure 3 is a 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] Markings in the figure are: 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 solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0045] In the manufacturing process of semiconductor packaging, two or more layers of thin films are deposited on the surface of the chip. In the implementation of this method, ideally, the roughness distribution of the upper and lower surfaces of the upper film is assumed to be consistent. In the case of multi-layer thin film deposition, if this method is used to measure the contact thermal resistance between two of the thin films, the measurement error will increase due to the large difference in the roughness distribution of the upper and lower surfaces of the upper film. Therefore, this method is mainly applicable to the case of two-layer thin film deposition.

[0046] Example 1

[0047] This embodiment provides a contact thermal resistance measurement method taking 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 topographic structure data of the upper surface of the lower film 3 and record the surface roughness distribution. The topographic structure data is represented by a three-dimensional matrix , where x 0 ,y 0 Respectively represent the horizontal and vertical coordinate values ​​of any point on the film surface, z 0 Indicates the height value of the point.

[0050] Step 2: After the upper film 1 is deposited, the morphological 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 morphological 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. The roughness distribution of the lower surface of the upper film corresponds to the roughness distribution of its upper surface under ideal conditions, and the distribution function constructed by 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, that is, the lower surface condition and distribution function can be obtained through the upper surface roughness condition 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 of the characteristic size of the film surface. n represents the number of iterations, which is used to construct the fractal surface. In the actual calculation process, as n increases, the contribution of each item to the total surface height will gradually decrease. When the iteration causes the surface height change to be no longer significant, the iteration is stopped.

[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 It is 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 morphological 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 it rotates 360°.

[0078] Step 5: According to 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 thermal contact 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 film and the upper film 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 of the upper surface of the lower film 3 is a=0.4, the frequency growth coefficient is b=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 in 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 model of the film interface contact 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 final initial void ratio was 23.76%.

[0092] Step 3: Calculate the change in void ratio by adjusting the relative angles of 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 range of the void ratio 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 their corresponding contact thermal resistances.

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

[0096] like Figure 5 As shown in the figure, by measuring the contact thermal resistance of the finite element model with different void proportions, the relationship between the void proportion 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 proportion of the interface of three different material films is tested, namely tungsten (W) and silicon dioxide (SiO 2 ) interface, tungsten (W) and silicon (Si) interface, tungsten (W) and copper (Cu) interface. In the three interfaces, it can be clearly seen that the void ratio is different for tungsten (W) and silicon dioxide (SiO 2 ) has the greatest impact on the interface contact thermal resistance, and has less impact on 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 a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, 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 disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[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 box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes 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 generate 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 capable of directing a computer or other programmable data processing device to operate 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 A 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 operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified 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 morphological structure data of the upper surface of the lower film, and constructing a surface distribution function of the lower film according to the morphological structure data of the upper surface of the lower film; After the upper film is deposited, the morphological structure data of the upper surface of the upper film is obtained, and the surface distribution function of the upper film is constructed according to 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; Based on the morphological structure 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 at 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 through 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 coordinates of any point on the film surface, respectively, and z0 represents the height of the point.

3. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The step of acquiring the topographic structure data of the upper surface of the upper film and constructing the surface distribution function of the upper film according to the topographic structure data of the upper surface of the upper film comprises: 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 morphological 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 comprises: 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 interface 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 three-dimensional image of the upper film 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 it rotates 360°.

9. The contact thermal resistance measurement method considering interface roughness distribution according to claim 1, characterized in that: The thermal contact 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 film and the upper film respectively.

Images