Metal dielectric contact thermal resistance test method and test device considering volume shrinkage

Abstract

The present invention discloses a metal-medium contact thermal resistance testing method and testing device that takes volume shrinkage into account. The testing method includes establishing a metal / medium contact thermal resistance model; obtaining the strain distribution of the metal / medium interface; calculating the displacement field of the interface; calculating the equivalent average displacement of the entire interface; simulating the interface to produce the same average displacement to obtain the load size at this time; applying the same load to the actual model to produce an equivalent average displacement at the interface of the actual model; and measuring the contact thermal resistance of the actual model to obtain the interface contact thermal resistance of the actual model. The present invention takes into account the impact of the volume shrinkage problem caused by the process on the contact thermal resistance, and at the same time solves the problem of the difficulty in measuring the metal / medium interface contact thermal resistance in actual production through modeling and simulation methods. The method provided by the present invention can provide a theoretical basis for testing the metal / medium contact thermal resistance during the packaging process.

Description

Technical Field

[0001] The present invention relates to the technical field of thermal characteristics research in a semiconductor manufacturing process, and in particular to a metal dielectric contact thermal resistance testing method and testing device taking volume shrinkage into consideration. Background Art

[0002] 3D NAND is a new flash memory technology that increases storage density by vertically stacking memory cells, thereby providing more storage capacity within a limited space. Deposition processes play a crucial role in the fabrication of semiconductor devices such as 3D NAND. They are primarily used to form thin films on or within the chip, which 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] At present, the measurement method of contact thermal resistance mainly involves idealizing the metal / medium model and directly measuring the contact thermal resistance. It does not consider the impact of volume shrinkage caused by different thermal expansion coefficients of materials during the process on the contact thermal resistance, resulting in inaccuracy in the measured contact thermal resistance. It is difficult to provide an effective theoretical basis for testing the metal / medium contact thermal resistance during the packaging process. Summary of the Invention

[0004] The purpose of the present invention is to address the problems existing in the prior art and to provide a metal medium contact thermal resistance testing method and testing device taking volume shrinkage into consideration.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for testing the contact thermal resistance of a metal medium taking volume shrinkage into consideration comprises the following steps:

[0007] Establishing a simulated metal / medium contact thermal resistance model and correcting the contact thermal resistance model by setting boundary conditions, etc.;

[0008] Obtain the strain distribution at the metal / dielectric interface;

[0009] According to the constitutive relationship of the material, the strain and displacement of the interface are related, and the displacement field of the interface is calculated by numerical methods;

[0010] Calculating the equivalent average displacement of the entire interface through the displacement field of the interface;

[0011] Applying a load to the metal / medium interface through simulation, simulating the same average displacement of the interface, and obtaining the load magnitude at this time;

[0012] Applying a load of the same magnitude to the actual metal / medium model so as to generate an equivalent average displacement at the interface of the actual metal / medium model;

[0013] The interface thermal contact resistance of the actual metal / medium model can be obtained by measuring the thermal contact resistance of the actual metal / medium model.

[0014] The present invention addresses the impact of process volume shrinkage on contact thermal resistance. Simultaneously, through modeling and simulation, it addresses the difficulty in measuring the metal / dielectric interface contact thermal resistance in actual production. This method provides a theoretical basis for measuring metal / dielectric contact thermal resistance during the packaging process. This method enables more accurate and reasonable data on metal / dielectric contact thermal resistance, optimizing existing measurement methods.

[0015] This metal-medium contact thermal resistance test method uses finite element software simulation modeling to more accurately obtain the stress-strain distribution and displacement of the metal / medium interface. It also analyzes the effect of material volume shrinkage on the interface contact thermal resistance during the process through equivalent calculation, reducing the difficulty of measuring the metal / medium contact thermal resistance.

[0016] Furthermore, a metal / medium contact thermal resistance model was established using finite element simulation software.

[0017] Furthermore, the strain distribution is obtained by simulating a deposition manufacturing process.

[0018] Furthermore, the relationship between interface strain and displacement is as follows:

[0019] The material constitutive relation describes the relationship between stress and strain. For linear elastic materials, it is:

[0020] ,

[0021] Where, is the stress tensor, is the strain tensor, is the elastic modulus tensor;

[0022] For small deformations, the relationship between the displacement gradient and the strain tensor is expressed as:

[0023] ,

[0024] Where, 、 is the displacement component, 、 are coordinates;

[0025] According to Newton's second law, the equilibrium equation of the contact thermal resistance model is expressed as:

[0026] ,

[0027] Where, is the volume force, is the material density, is the acceleration.

[0028] Furthermore, the method for solving the displacement field is as follows:

[0029] The finite element method is used to discretize the continuous domain into finite elements and approximate the displacement field on each element. First, the structure is divided into a finite number of elements, each element has a node and shape function, and then the local stiffness matrix is ​​calculated. For each element, the local stiffness matrix is ​​calculated based on the shape function and material properties of each element. , the calculation formula is:

[0030] ,

[0031] Where B is the shape function matrix, C is the elastic matrix of the material, is the volume of an element, and e indicates an element;

[0032] After obtaining the local stiffness matrices of all elements, they are assembled into the global stiffness matrix K:

[0033] ,

[0034] After obtaining the global stiffness matrix, the global load vector is assembled according to the boundary conditions and loads of the contact thermal resistance model. :

[0035] , is the local load vector,

[0036] Finally, the global stiffness matrix and global load vector are solved to obtain the global displacement vector u:

[0037] ,

[0038] After the global displacement vector is calculated, the average displacement of the entire interface is calculated through the displacement of each point on the interface.

[0039] Furthermore, after the actual metal / medium model is made, one end of the actual metal / medium model is set as a cold end and a heat source is set on the other end, and a load is applied to the actual metal / medium model to cause the actual metal / medium model to displace at the interface.

[0040] Furthermore, during the 3D NAND fabrication process, different thin films are deposited between holes etched in the semiconductor device through a deposition manufacturing process to form a metal / dielectric contact interface between the holes; the thin film is one or more of an insulating layer, a conductive layer, and a semiconductor layer.

[0041] A testing device for a metal-medium contact thermal resistance testing method that takes volume shrinkage into account, the testing device comprising a detection platform, a first fixing member and a second fixing member provided on the detection platform, an actual metal / medium model disposed between the first fixing member and the second fixing member, a cold end and a heat source provided at each end of the actual metal / medium model, a load application assembly connected to the first fixing member or the second fixing member; controllers of the cold end, the heat source, and the load application assembly are also respectively connected to a computer.

[0042] Furthermore, the first fixing part is a suction cup, and the second fixing part is a clamp, the suction cup adsorbs one end surface of the actual metal / medium model, and the clamp clamps the other end of the actual metal / medium model; the heat source is a hot plate arranged outside the suction cup, and the cold end is a cold plate arranged on the end surface of the actual metal / medium model.

[0043] Furthermore, the heating plate is an electric heating plate and is connected to a heating controller; the suction cup is a vacuum suction cup or a magnetic suction cup, and the load application component is a tension rod provided with a mechanical sensor.

[0044] Compared with the prior art, the beneficial effects of the present invention are: 1. The metal-medium contact thermal resistance testing method uses simulation modeling to establish a contact thermal resistance model and takes into account the different volume shrinkage caused by different thermal expansion coefficients of materials during the process, which affects the interface state and thus the contact thermal resistance. The method first establishes a metal / medium model through simulation, and calculates the strain distribution of the interface during the process, and then derives the displacement field and equivalent average displacement of the interface. Finally, a load is applied to the metal / medium model through a designed fixture to generate an equivalent average displacement, and the contact thermal resistance of the final model is measured to obtain the metal / medium contact thermal resistance in actual production; the method can obtain the metal / medium contact thermal resistance data more accurately and reasonably, and optimizes the existing measurement method; 2. The feature of the present invention is that it takes into account the influence of the volume shrinkage problem caused by the process on the contact thermal resistance, and at the same time solves the problem of difficulty in measuring the metal / medium interface contact thermal resistance in actual production through modeling and simulation methods. The method provided by the present invention can provide a theoretical basis for testing the metal / medium contact thermal resistance during the packaging process. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A process mechanics model of the 3D NAND core structure provided by an embodiment of the present invention;

[0046] Figure 2 A 3D NAND structure simulation model provided by an embodiment of the present invention;

[0047] Figure 3 A word line structure diagram provided by an embodiment of the present invention;

[0048] Figure 4 This is a schematic diagram of a metal medium contact thermal resistance testing device taking volume shrinkage into consideration according to the present invention;

[0049] In the figure: 1. Load application assembly; 2. Fixture; 3. Cold plate; 4. Metal; 5. Medium (4 and 5 together are a schematic diagram of the metal / medium model); 6. Suction cup; 7. Hot plate; 8. Heating controller; 9. Testing platform; 10. Computer. DETAILED DESCRIPTION

[0050] The following will clearly and completely describe the technical solution of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0051] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limiting the present invention. Furthermore, the terms "first," "second," etc., etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0052] Combine Figures 1 to 3 As shown, a method for testing the contact thermal resistance of a metal medium taking volume shrinkage into consideration is provided, and the testing method comprises the following steps:

[0053] Step 1: Using finite element simulation software to establish a metal / medium contact thermal resistance model, and calibrating the contact thermal resistance model by setting boundary conditions, etc.;

[0054] Step 2: obtaining the strain distribution by simulating the deposition manufacturing process;

[0055] Step 3: According to the material constitutive relationship, the strain and displacement of the interface are related, and then the displacement field of the interface is calculated by numerical methods (such as finite element method FEM);

[0056] Step 4: Calculate the equivalent average displacement of the entire interface through the displacement field of the interface;

[0057] Step 5: Apply a load to the metal / medium interface through simulation, simulate the interface to produce the same average displacement, and obtain the load magnitude at this time;

[0058] Step 6: Design a test device and make an actual metal / medium model, and use the test device to apply the same load to the actual metal / medium model so that an equivalent average displacement is generated at the interface of the actual metal / medium model;

[0059] Step 7: Measuring the thermal contact resistance of the actual metal / medium model under the action of the test device can obtain the interface thermal contact resistance of the actual metal / medium model.

[0060] This metal-medium contact thermal resistance testing method uses simulation modeling to establish a contact thermal resistance model and takes into account the impact of different volume shrinkage caused by different thermal expansion coefficients of materials during the process, which affects the interface state and thus the contact thermal resistance. This method first establishes a metal / medium model through simulation and calculates the strain distribution of the interface during the process, and then derives the displacement field and equivalent average displacement of the interface. Finally, a load is applied to the metal / medium model through a designed fixture to generate an equivalent average displacement, and the contact thermal resistance of the final model is measured to obtain the metal / medium contact thermal resistance in actual production. This method can obtain metal / medium contact thermal resistance data more accurately and reasonably, optimizing the existing measurement method.

[0061] The characteristic of the present invention is that it takes into account the influence of volume shrinkage caused by the process on the contact thermal resistance, and solves the problem of difficulty in measuring the contact thermal resistance of the metal / medium interface in actual production through modeling and simulation methods. The method provided by the present invention can provide a theoretical basis for testing the metal / medium contact thermal resistance during the packaging process.

[0062] This metal-medium contact thermal resistance test method uses finite element software simulation modeling to more accurately obtain the stress-strain distribution and displacement of the metal / medium interface. It also analyzes the effect of material volume shrinkage on the interface contact thermal resistance during the process through equivalent calculation, reducing the difficulty of measuring the metal / medium contact thermal resistance.

[0063] The method for calculating stress, strain and interface displacement according to the material constitutive relationship in the above step 3 is as follows.

[0064] The constitutive relation of the material describes the relationship between stress and strain. For linear elastic materials, it is:

[0065] ,

[0066] Where, is the stress tensor, is the strain tensor, is the elastic modulus tensor;

[0067] For small deformations, the relationship between the displacement gradient and the strain tensor is expressed as:

[0068] ,

[0069] Where, 、 is the displacement component, 、 are coordinates;

[0070] According to Newton's second law, the equilibrium equation of the contact thermal resistance model is expressed as:

[0071] ,

[0072] Where, is the volume force, is the material density, is the acceleration.

[0073] Furthermore, the method for solving the displacement field is as follows:

[0074] The finite element method is used to discretize the continuous domain into finite elements and approximate the displacement field on each element. First, the structure is divided into a finite number of elements, each element has a node and shape function, and then the local stiffness matrix is ​​calculated. For each element, the local stiffness matrix is ​​calculated based on the shape function and material properties of each element. , the calculation formula is:

[0075] ,

[0076] Where B is the shape function matrix, C is the elastic matrix of the material, is the volume of the element;

[0077] After obtaining the local stiffness matrices of all elements, they are assembled into the global stiffness matrix K:

[0078] ,

[0079] After obtaining the global stiffness matrix, the global load vector is assembled according to the boundary conditions and loads of the contact thermal resistance model. :

[0080] , is the local load vector,

[0081] Finally, the global stiffness matrix and global load vector are solved to obtain the global displacement vector u:

[0082] , to solve this linear equation system, direct solution methods such as Gaussian elimination method, or iterative solution methods such as conjugate gradient method, generalized minimum residual method, etc. can be used.

[0083] After the global displacement vector is calculated, the average displacement of the entire interface is calculated through the displacement of each point on the interface.

[0084] Figure 1 Various mechanical models of 3D NAND structures are shown, including a) a multi-layer stacked structure, b) step-by-step etching and oxide deposition, c) hole etching on the structure, d) ONO and filler deposition, e) powder etching and WL forming, and f) tungsten deposition structure.

[0085] During the 3D NAND fabrication process, different thin films are deposited between the holes etched in the semiconductor device through a deposition process to form a metal / dielectric contact interface between the holes; the thin films are one or more of an insulating layer, a conductive layer, and a semiconductor layer.

[0086] Figure 2 The figure shows a certain 3D NAND simulation model, which is a microscopic enlarged schematic diagram. The unit of the diameter of each cylinder in the figure is nm. For example, from the inner circle to the outer circle, they are Φ12nm, Φ18nm, Φ28nm, Φ38nm and Φ48nm. The colors represent different materials. From the inner circle to the outer circle, they are SiO2, Si, SiO2, Si3N4, SiO2 and W.

[0087] Figure 3 It is the word line structure diagram of the simulation model, where a) is the equivalent stress cloud diagram; b) is the displacement cloud diagram, U2 is the displacement; c) and d) are both stress cloud diagrams, and the subscripts 123 represent xyz respectively, S11 represents the stress in the positive direction, and S23 represents the shear stress in the yz plane.

[0088] like Figure 4 As shown, a testing device for a metal-medium contact thermal resistance testing method taking volume shrinkage into account is provided. The testing device includes a detection platform 9, on which a first fixing member and a second fixing member are provided. The actual metal / medium model is arranged between the first fixing member and the second fixing member. A cold end and a heat source are provided at both ends of the actual metal / medium model, respectively. The first fixing member or the second fixing member is connected to a load applying component 1; the controllers of the cold end, the heat source and the load applying component are also connected to a computer 10, respectively.

[0089] This testing device can fix and clamp the metal / medium model on the detection platform through the arrangement of the first fixing member and the second fixing member. The load application assembly applies a tensile force to one of the first fixing member and the second fixing member, causing the actual metal / medium model to produce a very small displacement at the contact interface. The magnitude of the applied tensile force is determined based on the load magnitude obtained in step 5 of the testing method, so that the actual metal / medium model can also attempt an equivalent displacement. At this time, data such as the temperature at the cold end and the heat source, the temperature of the metal / medium, and the heat transfer can also be recorded for subsequent contact thermal resistance calculation.

[0090] The actual metal / medium model is provided with a cold end and a heat source at both ends, respectively, which can form a temperature difference at both ends. When performing heat transfer calculation on the interface thermal resistance of the actual model, the effect of the volume change of the actual model on the interface can be ignored because the effect of interface shrinkage on the contact thermal resistance has been considered when calculating the equivalent mean displacement of the interface in the previous step.

[0091] The actual metal / dielectric model is a simplified model structure that is actually made. This model is also prepared by a deposition process. Compared with the theoretical model, its deposition layer is significantly thicker. At the same time, the clamping end of the fixture used in this structure is also relatively small, so that it can be clamped by a fixture in actual operation. Figure 4 The scale in the figure is slightly exaggerated for illustration; this allows the load to generate microscopic displacement at the interface, so that the measurement test can be carried out while taking into account the volume change of the material.

[0092] Furthermore, the first fixing member is a suction cup 6, and the second fixing member is a clamp 2. The suction cup 6 and clamp 2 can secure different types of materials, such as dielectrics 5 and metals 4, and are easy to operate. The suction cup 6 adheres to one end of the actual metal / dielectric model, while the clamp 2 clamps the other end of the actual metal / dielectric model. The heat source is a hot plate 7 located outside the suction cup 6, and the cold end is a cold plate 3 located on the end of the actual metal / dielectric model.

[0093] Furthermore, the hot plate 7 is an electric heating plate and is connected to a heating controller 8; the cold plate 3 is a plate-shaped or disc-shaped structure, and the function of the cold plate is to receive heat transferred through the actual model of the metal medium in order to calculate the heat amount and the interface thermal resistance; the cold plate can be connected to a temperature sensor, which can obtain the temperature of the cold end in real time; before the experiment starts, the temperature of both ends of the actual model can be adjusted to keep both ends at room temperature before starting the experiment; the suction cup 6 is a vacuum suction cup or a magnetic suction cup, and the load application component 1 is a tension rod provided with a mechanical sensor, and the load is applied by an external power source.

[0094] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A metal dielectric contact thermal resistance test method considering volume shrinkage, characterized in that: The testing method comprises the following steps: Establishing a simulated metal / medium contact thermal resistance model and correcting the contact thermal resistance model by setting boundary conditions; Obtain the strain distribution at the metal / dielectric interface; According to the constitutive relationship of the material, the strain and displacement of the interface are related, and the displacement field of the interface is calculated by numerical methods; Calculating the equivalent average displacement of the entire interface through the displacement field of the interface; Applying a load to the metal / medium interface through simulation, simulating the interface to produce the same equivalent average displacement, and obtaining the load magnitude at this time; Applying a load of the same magnitude to the actual metal / medium model so as to generate an equivalent average displacement at the interface of the actual metal / medium model; The interface thermal contact resistance of the actual metal / medium model can be obtained by measuring the thermal contact resistance of the actual metal / medium model.

2. The metal medium contact thermal resistance testing method considering volume shrinkage according to claim 1, characterized in that: The metal / medium contact thermal resistance model is established using finite element simulation software.

3. The metal medium contact thermal resistance testing method considering volume shrinkage according to claim 1, characterized in that: The strain distribution is obtained by simulating a deposition manufacturing process.

4. The metal medium contact thermal resistance testing method considering volume shrinkage according to claim 1, characterized in that: The relationship between interface strain and displacement is as follows: The material constitutive relation describes the relationship between stress and strain. For linear elastic materials, it is: ， Where, is the stress tensor, is the strain tensor, is the elastic modulus tensor; For small deformations, the relationship between the displacement gradient and the strain tensor is expressed as: ， Where, 、 is the displacement component, 、 are coordinates; According to Newton's second law, the equilibrium equation of the contact thermal resistance model is expressed as: ， Where, is the volume force, is the material density, is the acceleration.

5. The metal medium contact thermal resistance testing method considering volume shrinkage according to claim 1, characterized in that: The solution method of the displacement field is as follows: The finite element method is used to discretize the continuous domain into finite elements and approximate the displacement field on each element. First, the structure is divided into a finite number of elements, each element has a node and shape function, and then the local stiffness matrix is ​​calculated. For each element, the local stiffness matrix is ​​calculated based on the shape function and material properties of each element. , the calculation formula is: ， Where B is the shape function matrix, C is the elastic matrix of the material, is the volume of the element; After obtaining the local stiffness matrices of all elements, they are assembled into the global stiffness matrix K: ， After obtaining the global stiffness matrix, the global load vector is assembled according to the boundary conditions and loads of the contact thermal resistance model. : , is the local load vector, Finally, the global stiffness matrix and global load vector are solved to obtain the global displacement vector u: ， After the global displacement vector is calculated, the average displacement of the entire interface is calculated through the displacement of each point on the interface.

6. The metal medium contact thermal resistance testing method considering volume shrinkage according to claim 1, characterized in that: After the actual metal / medium model is made, one end of the actual metal / medium model is set as a cold end and the other end is set as a heat source, and a load is applied to the actual metal / medium model to cause the actual metal / medium model to displace at the interface.

7. The metal medium contact thermal resistance testing method considering volume shrinkage according to claim 3, characterized in that: During the 3D NAND fabrication process, different thin films are deposited between the holes etched in the semiconductor device through a deposition manufacturing process to form a metal / dielectric contact interface between the holes; The thin film is one or more of an insulating layer, a conductive layer and a semiconductor layer.

8. A testing device for the metal medium contact thermal resistance testing method considering volume shrinkage according to any one of claims 1 to 7, characterized in that: The testing device includes a detection platform, on which a first fixing member and a second fixing member are provided. The actual metal / medium model is arranged between the first fixing member and the second fixing member. A cold end and a heat source are provided at both ends of the actual metal / medium model, respectively. The first fixing member or the second fixing member is connected to a load application component. The controllers of the cold end, the heat source, and the load application component are also connected to a computer, respectively.

9. The testing device for the metal medium contact thermal resistance testing method considering volume shrinkage according to claim 8, characterized in that: The first fixing part is a suction cup, and the second fixing part is a clamp. The suction cup absorbs one end surface of the actual metal / medium model, and the clamp clamps the other end of the actual metal / medium model. The heat source is a hot plate arranged outside the suction cup, and the cold end is a cold plate arranged on the end surface of the actual metal / medium model.

10. The testing device for the metal medium contact thermal resistance testing method considering volume shrinkage according to claim 9, characterized in that: The heating plate is an electric heating plate and is connected to a heating controller; the suction cup is a vacuum suction cup or a magnetic suction cup; and the load application component is a tension rod provided with a mechanical sensor.

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