Silicone-based resin composition and semiconductor device containing said silicone-based resin composition
The silicone-based resin composition with dendritic and spherical particles stabilizes thermal conductivity and adhesion, addressing unreliable heat dissipation in electronic components by maintaining consistent performance under varying pressures.
Patent Information
- Application Number
- JP2025540516
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-01-11
- Publication Date
- 2026-01-13
AI Technical Summary
Existing thermally conductive materials exhibit varying thermal conductivity properties based on pressurization conditions, leading to unreliable heat dissipation and performance in electronic components.
A silicone-based resin composition comprising a conductive filler with dendritic and spherical particles, and organic polysiloxane, maintaining a specific particle size uniformity and content ratio to stabilize thermal conductivity and improve adhesion.
The composition achieves stable thermal conductivity and durability by minimizing fluctuations under different pressure conditions, ensuring reliable heat dissipation and preventing voids or cracks.
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Figure 2026501029000001_ABST
Abstract
Description
[Technical Field]
[0001] The present invention relates to a silicone resin composition and a semiconductor device containing the silicone resin composition. [Background technology]
[0002] Many electronic components generate heat during use, and it is necessary to remove this heat in order to ensure their normal operation. In particular, integrated circuit elements such as CPUs used in personal computers generate more heat as their operating frequencies increase, making heat management an important issue.
[0003] For this reason, many methods for dissipating such heat have been proposed, and in particular, for electronic components that dissipate large amounts of heat, a method has been proposed in which a thermally conductive material such as thermally conductive grease or a thermally conductive sheet is interposed between the electronic component and a member such as a heat sink to dissipate the heat. Korean Patent Application Publication No. 10-2020-0086307 discloses a semiconductor device including a thermally conductive material.
[0004] However, in the case of thermally conductive materials manufactured by pressurizing a thermally conductive composition, even if the same thermally conductive composition is used, there is a problem that the thermal conductivity properties are expressed differently depending on the pressurization conditions, resulting in a decrease in the reliability of product performance. [Prior art documents] [Patent documents]
[0005] [Patent Document 1] Korean Patent Application Publication No. 10-2020-0086307 Summary of the Invention [Problem to be solved by the invention]
[0006] Therefore, the present invention has been made in consideration of the above problems, and has an object to provide a silicone-based resin composition that minimizes variation in thermal conductivity and has excellent heat dissipation properties and durability, and a semiconductor device that uses the silicone-based resin composition. [Means for solving the problem]
[0007] According to one embodiment of the present invention, the above and other objects are achieved by providing a conductive filler comprising a first conductive powder containing dendritic particles and a second conductive powder containing spherical particles, wherein the uniformity of the average particle size of the first conductive powder calculated according to the following formula 1 is 0.3 to 4.0, [Formula 1] (D 90 -D 50 ) / (D 50 -D 10 ) In the formula, D 10 is the diameter corresponding to 10% of the cumulative volume of the first conductive powder, and D 50 is the diameter corresponding to 50% of the cumulative volume of the first conductive powder, and D 90 is achieved by providing the conductive filler with a diameter corresponding to 90% of the cumulative volume of the first conductive powder.
[0008] According to another aspect of the present invention, there is provided a silicone-based resin composition comprising an organic polysiloxane and a conductive filler, wherein the rate of change in thermal conductivity measured by the following measurement method is 30% or less: [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2 The silicone resin composition was then hot-pressed for 15 minutes under the conditions of 165°C and 0.1 kgf / cm to produce a first sheet. 2 The mixture is hot-pressed for 15 minutes under the conditions of (a) to (c) to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (│TC 26 -TC 0.1 │ / TC 26 ) x 100 During the ceremony, T.C. 26 is the thermal conductivity of the first sheet sample (W / mK), and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample.
[0009] In one embodiment of the present invention, the silicone resin composition may contain the organic polysiloxane and the conductive filler in a weight ratio of 20:80 to 5:95.
[0010] In one embodiment of the present invention, the conductive filler may include a first conductive powder including dendritic particles and a second conductive powder including spherical particles.
[0011] In one embodiment of the present invention, the conductive filler may contain the first conductive powder and the second conductive powder in a weight ratio of 5:95 to 80:20.
[0012] In one embodiment of the present invention, the conductive filler may contain the first conductive powder and the second conductive powder in a weight ratio of 5:95 to 50:50.
[0013] In one embodiment of the present invention, the tap density of the first conductive powder is 0.1 g / cm 3 ~3.0g / cm 3 It could be.
[0014] In one embodiment of the present invention, the specific surface area of the first conductive powder is 0.2 m 2 / g~5.0m 2 / g.
[0015] In one embodiment of the present invention, the silicone resin composition may have a thermal conductivity per weight of the filler of 1 W / mK or more, as calculated by the following formula 3: [Formula 3] X / Y×10 In the formula, X is the thermal conductivity of the first sheet sample or the second sheet sample measured at 25°C, and Y is the weight percent of the conductive filler relative to the total weight of the silicone-based resin composition.
[0016] In one embodiment of the present invention, the thermal conductivity of the first sheet sample or the second sheet sample measured at 25° C. may be 10 W / mK or more.
[0017] According to yet another aspect of the present invention, there is provided a semiconductor device comprising a semiconductor package, a heat dissipation portion disposed on the semiconductor package, and a thermally conductive layer interposed between the semiconductor package and the heat dissipation portion, wherein the thermally conductive layer comprises a silicone-based resin composition, the silicone-based resin composition comprises an organic polysiloxane and a conductive filler, and a rate of change in thermal conductivity of the silicone-based resin composition measured by the following measurement method is 30% or less: [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2 The silicone resin composition was then hot-pressed for 15 minutes under the conditions of 165°C and 0.1 kgf / cm to produce a first sheet. 2 The mixture is hot-pressed for 15 minutes under the conditions of (a) to (c) to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (│TC 26-TC 0.1 │ / TC 26 ) x 100 During the ceremony, T.C. 26 is the thermal conductivity of the first sheet sample (W / mK), and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample, [Effects of the Invention]
[0018] The silicone resin composition of the present invention exhibits a thermal conductivity value that allows it to exhibit appropriate heat dissipation function even when commercialized under different pressure conditions, and since the thermal conductivity fluctuations are small, the reliability of product performance can be improved.
[0019] Furthermore, since the conductive filler has a uniform average particle size and contains conductive particles of different shapes in a specific content ratio, the formation of an electrical network between the particles can be improved, and the silicone-based resin composition exhibits high thermal conductivity even when the conductive filler content is low.
[0020] Furthermore, because the organic polysiloxane and conductive filler are contained in a specific content ratio, good adhesion to the adherend can be maintained and voids and cracks caused by thermal shock do not occur, resulting in excellent durability. [Brief explanation of the drawings]
[0021] [Figure 1] FIG. 1 is a diagram showing the steps of a method for measuring the thermal conductivity of the silicone resin composition of the present invention. [Figure 2] FIG. 2 is a diagram schematically illustrating a semiconductor device of the present invention. DETAILED DESCRIPTION OF THE INVENTION
[0022] The structural or functional descriptions of the embodiments disclosed in this specification or application are merely examples for explaining embodiments according to the technical idea of the present invention, and the embodiments according to the technical idea of the present invention may be implemented in various forms other than the embodiments disclosed in this specification or application, and the technical idea of the present invention should not be construed as being limited to the embodiments described in this specification or application.
[0023] Furthermore, in this specification or application, when a certain component is "included" or "comprised," it does not mean that other components may be further included or included, and that other components are excluded, unless otherwise specified. Also, it should be understood that all numerical ranges expressing physical property values, dimensions, etc. of components described in this specification or application are always modified by the term "about" unless otherwise specified.
[0024] The conductive filler and silicone resin composition of the present invention, as well as the semiconductor device containing the conductive filler and silicone resin composition, will be described below.
[0025] <Conductive filler> The conductive filler of the present invention comprises a first conductive powder containing dendritic particles and a second conductive powder containing spherical particles, and the uniformity of the average particle size of the first conductive powder calculated according to the following formula 1 is 0.3 to 4.0. [Formula 1] (D 90 -D 50 ) / (D 50 -D 10 ) In the formula, D 10 is the diameter corresponding to 10% of the cumulative volume of the first conductive powder, and D 50 is the diameter corresponding to 50% of the cumulative volume of the first conductive powder, and D 90 is the diameter corresponding to 90% of the cumulative volume of the first conductive powder.
[0026] D 10 , D50 and D 90 can be measured using laser diffraction, which can generally measure particle sizes in the range of a few nanometers to a few millimeters and provides highly reproducible and high-resolution results.
[0027] When the uniformity of the average particle size calculated according to Equation 1 falls within the above range, it means that the size of the dendritic particles with a large specific surface area is uniform. Therefore, when a conductive filler is blended into a silicone-based resin composition and used as a thermally conductive material, the electrical network between the conductive filler particles becomes smooth, and high thermal conductivity can be achieved even when the conductive filler content is low.
[0028] <Silicone-based resin composition> The silicone resin composition of the present invention contains an organic polysiloxane and a conductive filler, and exhibits a rate of change in thermal conductivity of 30% or less as measured by the following measurement method. [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2 The silicone resin composition was then hot-pressed for 15 minutes under the conditions of 165°C and 0.1 kgf / cm to produce a first sheet. 2 The mixture is hot-pressed for 15 minutes under the conditions of (a) to (c) to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (│TC 26 -TC 0.1 │ / TC 26 ) x 100 During the ceremony, T.C. 26is the thermal conductivity of the first sheet sample (W / mK), and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample.
[0029] The silicone resin composition contains an organic polysiloxane.
[0030] The organic polysiloxane is represented by the following formula 1. [Formula 1] R 1 a SiO b In the formula, R 1 represents one or more groups selected from the group consisting of a hydrogen atom, a hydroxyl group, and a saturated or unsaturated monovalent hydrocarbon group having 1 to 18 carbon atoms, and a can be from about 1.8 to about 2.2, and a+b can be from about 3.5 to about 8.
[0031] a+b can be 4.
[0032] In Formula 1, the saturated or unsaturated monovalent hydrocarbon group having 1 to 18 carbon atoms may be an alkyl group such as a methyl group, ethyl group, propyl group, hexyl group, octyl group, decyl group, dodecyl group, tetradecyl group, hexadecyl group, or octadecyl group; a cycloalkyl group such as a cyclopentyl group or cyclohexyl group; an alkenyl group such as a vinyl group or allyl group; an aryl group such as a phenyl group or tolyl group; an aralkyl group such as a 2-phenylethyl group or 2-methyl-2-phenylethyl group; or a halogenated hydrocarbon group such as a 3,3,3-trifluoropropyl group, a 2-(perfluorobutyl)ethyl group, a 2-(perfluorooctyl)ethyl group, or a p-chlorophenyl group.
[0033] The weight-average molecular weight of the organic polysiloxane can be about 40,000 g / mol to about 80,000 g / mol, about 30,000 g / mol to about 100,000 g / mol, about 500 g / mol to about 10,000 g / mol, about 700 g / mol to about 7,000 g / mol, about 1,000 g / mol to about 5,000 g / mol, or about 1,500 g / mol to about 3,000 g / mol. The weight-average molecular weight can be measured in polystyrene equivalent terms.
[0034] The organic polysiloxane has a kinematic viscosity of 10 mm at 25°C. 2 / s~100,000mm 2 / s, 20,000mm 2 / s~100,000mm 2 / s, or approximately 30 mm 2 / s~approx. 10,000mm 2 The kinematic viscosity of the organopolysiloxane may be a value measured at 25°C using an Ostwald viscometer.
[0035] When the weight average molecular weight and kinematic viscosity of the organic polysiloxane are within the above ranges, an appropriate adhesive strength to the adherend can be maintained, and voids and cracks due to thermal shock do not occur, improving durability.
[0036] The organopolysiloxane may include a first organopolysiloxane.
[0037] The first organopolysiloxane contains alkenyl groups bonded to silicon atoms, and the number of alkenyl groups present in one molecule of the first organopolysiloxane can be at least 2, 2 to 10, 2 to 5, or 2.
[0038] The first organic polysiloxane is represented by the following formula 2. [Formula 2] R 1 a R 2 c SiO b In the formula, R 1can be a hydrogen atom, a hydroxyl group, or a saturated or unsaturated monovalent hydrocarbon group having 1 to 18 carbon atoms; R 2 may be an alkenyl group. In Formula 2, a+c may be about 1.8 to about 2.2, and a+b+c may be about 3.5 to about 8. In Formula 2, a+b+c may be about 4. In Formula 2, a may be about 1.8 to about 2.2. In Formula 2, c may be 0.0001 to 0.1.
[0039] The first organic polysiloxane is represented by the following formula 3. [ka] In the formula, R 1 can be a hydrogen atom, a hydroxyl group, or a saturated or unsaturated monovalent hydrocarbon group having 1 to 18 carbon atoms; R 2 may be an alkenyl group. In addition, in formula 3, n may be 1 to 1,500, and m may be 0 to 20. In addition, in formula 3, n may be 10 to 1,000, and m may be 0 to 20.
[0040] The first organic polysiloxane is represented by the following formula 4. [ka] In the formula, n can be 1 to 1,500, or 10 to 1,000.
[0041] The weight average molecular weight (Mw) of the first organopolysiloxane can be about 500 g / mol to about 10,000 g / mol, about 700 g / mol to about 7,000 g / mol, about 1,000 g / mol to about 5,000 g / mol, or about 1,500 g / mol to about 3,000 g / mol. The weight average molecular weight can be measured in polystyrene equivalent.
[0042] The first organopolysiloxane may have a kinematic viscosity of 10 cPs to 100,000 cPs, 30 cPs to 50,000 cPs, or 10,000 cPs to 40,000 cPs at 23° C. The kinematic viscosity of the first organopolysiloxane may be a value measured at 25° C. using an Ostwald viscometer.
[0043] The organopolysiloxane may include a second organopolysiloxane.
[0044] The second organopolysiloxane may contain hydrogen groups bonded to silicon atoms. The number of hydrogen groups per molecule of the second organopolysiloxane may be 1 to 10, 2 to 10, 2 to 5, or 2.
[0045] The second organopolysiloxane is represented by the following formula 5. [ka] In the formula, R 1 can be a hydrogen atom, a hydroxyl group, or a saturated or unsaturated monovalent hydrocarbon group having 1 to 18 carbon atoms; R 3 may be a hydrogen atom. In addition, in formula 5, n may be 1 to 1,500, and m may be 0 to 20. In addition, in formula 5, n may be 10 to 1,000, and m may be 0 to 20. In addition, in formula 5, n may be 1 to 1,500, and m may be 0.
[0046] The second organopolysiloxane is represented by the following formula 6. [ka]
[0047] The second organopolysiloxane may have a viscosity at about 23°C of about 500 cPs to about 5,000 cPs, about 500 cPs to about 3,000 cPs, or about 500 cPs to about 2,000 cPs.
[0048] The organopolysiloxane may further include a third organopolysiloxane, which is represented by the following formula 7: [ka] In the formula, R 1 can be a hydrogen atom, a hydroxyl group, or a saturated or unsaturated monovalent hydrocarbon group having 1 to 18 carbon atoms; R 3 may be a hydrogen atom. In addition, in formula 7, n may be 1 to 1,500, and m may be 1 to 500. In addition, in formula 7, n may be 10 to 1,000, and m may be 1 to 100.
[0049] The third organopolysiloxane is represented by the following formula 8. [ka] In the formula, n can be 1 to 1,500, and m can be 1 to 500. In addition, in formula 8, n can be 10 to 1,000, and m can be 1 to 100.
[0050] The third organopolysiloxane may have a viscosity at about 23°C of about 50 cPs to about 1,000 cPs, about 100 cPs to about 500 cPs, or about 100 cPs to about 500 cPs.
[0051] The ratio of the viscosity of the first organopolysiloxane to the viscosity of the second organopolysiloxane can be from 10:1 to 40:1.
[0052] Furthermore, the ratio of the viscosity of the second organopolysiloxane to the viscosity of the third organopolysiloxane can be from 2:1 to 10:1.
[0053] The content of the first organopolysiloxane can be about 60 parts by weight to about 90 parts by weight, about 70 parts by weight to about 85 parts by weight, or about 75 parts by weight to about 85 parts by weight, based on 100 parts by weight of the total organopolysiloxane.
[0054] The content of the second organic polysiloxane can be about 10 parts by weight to about 40 parts by weight, about 10 parts by weight to about 30 parts by weight, or about 12 parts by weight to about 23 parts by weight, relative to 100 parts by weight of the first organic polysiloxane.
[0055] The content of the third organic polysiloxane can be about 3 parts by weight to about 20 parts by weight, about 3 parts by weight to about 15 parts by weight, or about 4 parts by weight to about 10 parts by weight, relative to 100 parts by weight of the first organic polysiloxane.
[0056] When the silicone-based resin composition contains the first organic polysiloxane, the second organic polysiloxane, and the third organic polysiloxane within the above ranges, appropriate adhesive strength to the adherend is maintained, and the silicone-based resin composition can be spread evenly during the coating process.
[0057] The silicone-based resin composition contains a conductive filler.
[0058] The conductive filler may include a first conductive powder including dendritic particles and a second conductive powder including spherical particles. The first conductive powder may include a first silver powder. The first silver powder may include dendritic silver particles. The first silver powder may include surface-treated dendritic silver particles. The first silver powder may include copper-coated dendritic silver particles.
[0059] The tap density of the first conductive powder is 0.1 g / cm 3 ~3.0g / cm 3 , 0.1g / cm 3 ~2.0g / cm 3 , 0.1g / cm 3 ~1.8g / cm 3 , 0.1g / cm 3 ~1.6g / cm 3 , 0.2g / cm 3 ~1.6g / cm 3 , 0.3g / cm 3 ~1.6g / cm 3 , or 0.4 g / cm3 ~1.6g / cm 3 It could be.
[0060] To determine tap density, weigh 100 g of silver powder and gently drop it into a 100 ml measuring cylinder using a funnel. Then, place the measuring cylinder in a tap density measuring device and drop it 60 times per minute at a drop distance of 20 mm for 600 cycles to compress the silver powder. The tap density can be calculated from the volume of the compressed powder.
[0061] The specific surface area of the first conductive powder is 0.2 m 2 / g~5.0m 2 / g, 0.3m 2 / g~5.0m 2 / g, 0.4m 2 / g~5.0m 2 / g, 0.5m 2 / g~5.0m 2 / g, 0.7m 2 / g~5.0m 2 / g, 0.9m 2 / g~5.0m 2 / g, 1.0m 2 / g~5.0m 2 / g, 1.2m 2 / g~5.0m 2 / g, 1.4m 2 / g~5.0m 2 / g, 1.4m 2 / g~4.8m 2 / g, or 1.4m 2 / g~4.5m 2 / g.
[0062] To determine the specific surface area, take approximately 2 g of silver powder as a sample, degas it at 60±5°C for 10 minutes, and then measure the total surface area using an automatic specific surface area measuring device (BET method). Weigh the sample and calculate the specific surface area according to the following formula: Specific surface area (m 2 / g) = total surface area (m 2 ) / sample amount (g)
[0063] The aspect ratio of the dendritic silver particles contained in the first silver powder can be about 2-30, about 5-30, about 5-25, or about 5-20.
[0064] The first silver powder may be surface-treated with a surface treatment agent. The surface treatment agent may contain a C10 to C20 fatty acid. Examples of the fatty acid include capric acid, lauric acid, myristic acid, palmitic acid, stearic acid, arachidic acid, myristoleic acid, palmitoleic acid, sapienic acid, oleic acid, elaidic acid, vaccenic acid, linoleic acid, linoleic acid, arachidonic acid, eicosapentaenoic acid, and α-linolenic acid.
[0065] The loss on ignition (Ig-loss) of the first silver powder can be less than about 0.8 wt%, less than about 0.7 wt%, or less than about 0.6 wt%. Ig-loss can be measured at about 538°C for about 1 hour.
[0066] The surface of the first silver powder may be treated with a small amount of a surface treatment agent. That is, the first silver powder has a relatively low tap density and a large specific surface area, and may be surface-treated with a small amount of a surface treatment agent. Therefore, the first silver powder is uniformly dispersed in the organic polysiloxane, improving the thermal connection of the conductive filler. That is, because the first silver powder has improved dispersibility, it can be added to the organic polysiloxane in a high content. Furthermore, because the first silver powder has a dendritic surface area and the layer coated with the surface treatment agent is thin, the contact characteristics between the conductive fillers are improved. Therefore, the first silver powder can improve the thermal conductivity of the silicone-based resin composition.
[0067] The average particle size of the first silver powder can be about 0.5 μm to about 4 μm, about 1 μm to about 3 μm, or about 1.5 μm to about 2.5 μm.
[0068] The silicone resin composition may contain about 300 parts by weight to about 1,000 parts by weight, about 400 parts by weight to about 900 parts by weight, or about 500 parts by weight to about 800 parts by weight of the first silver powder per 100 parts by weight of the organic polysiloxane.
[0069] The second conductive powder may include a second silver powder. The second silver powder may include spherical silver particles. The second silver powder may include surface-treated spherical silver particles. The second silver powder may include copper-coated spherical silver particles.
[0070] The tap density of the second conductive powder is about 3.0 g / cm 3 Super, about 3.01g / cm 3 Super, about 4g / cm 3 Super, about 5g / cm 3 More than or about 5 g / cm 3 It is about 9 g / cm 3 It may be less than.
[0071] The specific surface area of the second conductive powder is approximately 1 m 2 / g or less, approximately 0.9m 2 / g or less, approximately 0.8m 2 / g or less, approximately 0.7m 2 / g or less, or about 0.6m 2 / g.
[0072] The aspect ratio of the spherical silver particles contained in the second silver powder can be about 1 to 2, about 1.2 to 1.7, or about 1.25 to 1.65.
[0073] The second silver powder may be surface-treated with a surface treatment agent, which may contain a C10 to C20 fatty acid.
[0074] The loss on ignition (Ig-loss) of the second silver powder can be less than about 0.8 wt.%, less than about 0.7 wt.%, or less than about 0.6 wt.%.
[0075] The average particle size of the second silver powder can be about 1.5 μm to about 5 μm, about 2 μm to about 4 μm, or about 2.5 μm to about 3.5 μm.
[0076] The silicone resin composition may contain about 100 parts by weight to about 800 parts by weight, about 150 parts by weight to about 700 parts by weight, or about 170 parts by weight to about 600 parts by weight of the second silver powder per 100 parts by weight of the organic polysiloxane.
[0077] The conductive filler may contain a first conductive powder and a second conductive powder in a weight ratio of 5:95 to 80:20, 5:95 to 60:40, or 5:95 to 50:50. Generally, even within the same silicone-based resin composition, the distribution characteristics of the conductive fillers contained within the silicone-based resin composition vary. Therefore, the applied pressure during the product manufacturing process can significantly affect the thermal conductivity of the final product. The conductive filler contains a first conductive powder and a second conductive powder containing particles with a different shape from the particles contained in the first conductive powder, improving the formation of an electrical network between the particles and improving thermal conductivity. Furthermore, the rate of change in thermal conductivity due to differences in applied pressure during the silicone-based resin composition manufacturing process is small, thereby improving the reliability of product performance. Furthermore, silicone-based resin compositions can exhibit high thermal conductivity even with a low filler content.
[0078] The silicone resin composition may contain the organic polysiloxane and the conductive filler in a weight ratio of 20:80 to 5:95, 20:80 to 6:94, or 20:80 to 10:90. By satisfying this range, good adhesion to the adherend is maintained and voids and cracks due to thermal shock are not generated, improving durability.
[0079] The silicone resin composition of the present invention has a rate of change in thermal conductivity of 30% or less as measured by the following measurement method. [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2The silicone resin composition was then hot-pressed for 15 minutes under the conditions of 165°C and 0.1 kgf / cm to produce a first sheet. 2 The mixture is hot-pressed for 15 minutes under the conditions of (a) to (c) to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (│TC 26 -TC 0.1 │ / TC 26 ) x 100 During the ceremony, T.C. 26 is the thermal conductivity of the first sheet sample (W / mK), and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample.
[0080] FIG. 1 is a diagram showing the steps of a method for measuring the thermal conductivity of the silicone resin composition of the present invention.
[0081] Referring to FIG. 1, each silicone resin composition 10 was supplied to a mold 20, and then (a-1) the silicone resin composition 10 was heated at 165° C. under a pressure of 26 kgf / cm. 2 (a-2) The silicone resin composition 10 was hot-pressed at 165°C and a pressure of 0.1 kgf / cm for 15 minutes to produce a first sheet 11. 2 The second sheet 12 is produced by hot pressing for 15 minutes under the conditions.
[0082] Next, (b) the first sheet 11 and the second sheet 12 are cured at 150°C for 2 hours to produce a first sheet sample 11-1 and a second sheet sample 11-2. The first sheet 11 and the second sheet 12 are placed in a drying oven 30 and cured.
[0083] Then, (c) the thermal conductivity of the first sheet sample 11-1 and the thermal conductivity of the second sheet sample 11-2 are measured at 25° C. using a sensor 40 in accordance with ISO 22007-2.
[0084] Next, the measured value of the thermal conductivity of the first sheet sample 11-1 and the measured value of the thermal conductivity of the second sheet sample 11-2 are substituted into Equation 1 to calculate the rate of change in thermal conductivity.
[0085] The rate of change in thermal conductivity of the silicone resin composition measured by the above-described measurement method may be 25% or less, 20% or less, 15% or less, or 10% or less.
[0086] Because the silicone-based resin composition has a rate of change in thermal conductivity, even when the silicone-based resin composition is commercialized under different pressure conditions, the rate of change in thermal conductivity varies little, ensuring reliable product performance. Furthermore, even when a product manufactured from the silicone-based resin composition is subjected to thermal shock, good adhesion to the adherend is maintained, and voids or cracks due to the thermal shock do not occur.
[0087] The silicone resin composition may have a thermal conductivity per weight of the filler, calculated by the following formula 3, of 1 W / mK or more, 1.05 W / mK or more, 1.07 W / mK or more, 1.1 W / mK or more, or 1.2 W / mK: [Formula 3] X / Y×10 (wherein X is the thermal conductivity of the first sheet sample or the second sheet sample measured at 25°C, and Y is the weight percent of the conductive filler based on the total weight of the silicone-based resin composition.)
[0088] The silicone-based resin composition has a thermal conductivity per weight of filler of 1 W / mK or more as calculated by Equation 3, and therefore can exhibit a relatively high thermal conductivity even when the silicone-based resin composition contains the same conductive filler.
[0089] The thermal conductivity of the first sheet sample or the second sheet sample measured at 25°C may be 10 W / mK or more, 10.1 W / mK or more, 10.2 W / mK or more, 10.3 W / mK or more, or 10.5 W / mK or more.
[0090] The first sheet sample or the second sheet sample made of the silicone-based resin composition has a thermal conductivity within the above-mentioned range, and therefore can exhibit appropriate heat dissipation function even when the silicone-based resin composition is commercialized under different pressure conditions.
[0091] The silicone resin composition may further contain a tackifier.
[0092] The tackifier may contain an alkoxysilane. The tackifier may also contain an epoxy group. The tackifier may also be at least one selected from the group consisting of 2-(3,4-epoxycyclohexyl)ethyltrimethoxysilane, 3-glycidoxypropylmethyldimethoxysilane, 3-glycidoxypropyltrimethoxysilane, 3-glycidoxypropylmethyldiethoxysilane, and 3-glycidoxypropyltriethoxysilane.
[0093] The silicone resin composition may contain a tackifier in an amount of about 1 to about 20 parts by weight, about 1 to about 10 parts by weight, or about 2 to about 8 parts by weight, per 100 parts by weight of the organic polysiloxane. The tackifier can improve the adhesive strength between the organic polysiloxane and the conductive filler.
[0094] The silicone-based resin composition may further contain a curing catalyst, which can accelerate the curing of the silicone-based resin composition.
[0095] The curing catalyst may be a platinum-based catalyst.
[0096] Examples of the curing catalyst include platinum-divinyltetramethyldisiloxane complexes, organic titanate esters such as tetrabutyl titanate and tetraisopropyl titanate; organic titanium chelate compounds such as diisopropoxybis(acetylacetate)titanium and diisopropoxybis(ethylacetoacetate)titanium; organic aluminum compounds such as aluminum tris(acetylacetonate) and aluminum tris(ethylacetoacetate); organic zirconium compounds such as zirconium tetra(acetylacetonate) and zirconium tetrabutylate; dibutyltin dioctoate, Examples of suitable organic compounds include organotin compounds such as dibutyltin dilaurate and butyltin-2-ethylhexoate; metal salts of organic carboxylic acids such as tin naphthenate, tin oleate, tin butyrate, cobalt naphthenate, and zinc stearate; amine compounds such as hexylamine and dodecylamine phosphate esters and their salts; quaternary ammonium salts such as benzyltriethylammonium acetate; alkali metal salts of lower fatty acids such as potassium acetate; dialkylhydroxylamines such as dimethylhydroxylamine and diethylhydroxylamine; and guanidyl group-containing organosilicon compounds.
[0097] The silicone resin composition may contain a curing catalyst in an amount of about 0.01 to about 5 parts by weight, about 0.03 to about 3 parts by weight, or about 0.1 to about 2 parts by weight per 100 parts by weight of the organic polysiloxane.
[0098] The silicone resin composition may further contain a reaction inhibitor, which may be at least one selected from the group consisting of acetylene compounds such as 2-methyl-3-butyn-2-ol, 2-phenyl-3-butyn-2-ol, and 1-ethynyl-1-cyclohexanol; ene-yne compounds such as 3-methyl-3-penten-1-yne and 3,5-dimethyl-3-hexen-1-yne; and curing reaction inhibitors such as hydrazine compounds, phosphine compounds, and mercaptan compounds.
[0099] The silicone resin composition may contain a reaction inhibitor in an amount of about 0.0001 to about 10 parts by weight per 100 parts by weight of the organic polysiloxane.
[0100] <Method of manufacturing silicone-based resin composition> The method for producing the silicone resin composition is not particularly limited, and known production methods can be used.
[0101] The silicone resin composition can be prepared by mixing, for example, organic polysiloxane, conductive filler, tackifier, curing catalyst, curing reaction inhibitor, etc. for 30 minutes to 4 hours using a mixer such as Trimix, Twinmix, or Planetary Mixer (all manufactured by Inoue Seisakusho Co., Ltd. and registered trademarks), Ultra Mixer (manufactured by Mizuho Industries Co., Ltd. and registered trademarks), or Hivis Dispermix (manufactured by Primix Corporation and registered trademarks). During the mixing process, the process temperature can be from about 0°C to about 25°C.
[0102] <Semiconductor device> FIG. 2 is a diagram schematically illustrating a semiconductor device of the present invention.
[0103] Referring to FIG. 2, the semiconductor device may include a circuit board 100, a semiconductor package 200, conductive bumps 300, a heat dissipation portion 400, and a thermally conductive layer 500.
[0104] The semiconductor device of the present invention comprises a semiconductor package 200, a heat dissipation section 400 disposed on the semiconductor package 200, and a thermally conductive layer 500 interposed between the semiconductor package 200 and the heat dissipation section 400, wherein the thermally conductive layer 500 comprises a silicone-based resin composition, the silicone-based resin composition comprises an organic polysiloxane and a conductive filler, and the rate of change in thermal conductivity of the silicone-based resin composition measured by the following measurement method is 30% or less: [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2The silicone resin composition was then hot-pressed for 15 minutes under the conditions of 165°C and 0.1 kgf / cm to produce a first sheet. 2 The mixture is hot-pressed for 15 minutes under the conditions of (a) to (c) to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (│TC 26 -TC 0.1 │ / TC 26 ) x 100 During the ceremony, T.C. 26 is the thermal conductivity of the first sheet sample (W / mK), and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample.
[0105] The specific method for measuring the rate of change in thermal conductivity of the silicone resin composition is the same as the method shown in FIG.
[0106] Since the silicone-based resin composition has a thermal conductivity change rate, the thermal conductive layer 500 containing the silicone-based resin composition has a small thermal conductivity change rate, thereby ensuring reliable product performance. Furthermore, even when the thermal conductive layer 500 is subjected to a thermal shock, good adhesion between the semiconductor package 200 and the heat dissipation part 400 is maintained, and voids or cracks due to the thermal shock do not occur.
[0107] The circuit board 100 may support the semiconductor package 200 , the conductive bumps 300 , the heat dissipation portion 400 and the thermally conductive layer 500 .
[0108] The circuit board 100 may include a circuit pattern. Alternatively, the circuit board 100 may include a plurality of circuit patterns inside a flat plate-shaped main body that includes an insulating and heat-resistant material and has a predetermined strength. Alternatively, the circuit board 100 may include connection pads that are arranged on the main body and are electrically connected to the circuit patterns.
[0109] For example, the main body of circuit board 100 may include a thermosetting resin substrate such as an epoxy resin substrate or a polyimide substrate, a flat plate, or a flat plate to which a heat-resistant organic film such as a liquid crystal polyester film or a polyamide film is attached. The circuit pattern may be arranged in a pattern inside the main body and may include power wiring for power supply, ground wiring, signal wiring for signal transmission, etc. The wiring may be arranged so as to be separated from each other by multiple interlayer insulating films formed on the top and bottom surfaces of the main body.
[0110] The connection pads may be exposed to the outside from the top surface of the main body, or may be connected to the circuit pattern. Therefore, an external connector connected to the circuit board 100 may be electrically connected to the internal circuit pattern via the connection pads.
[0111] Various electronic components may be mounted on the connection pads included in the circuit board 100. In other words, the circuit board 100 may be a system board on which electronic components including the semiconductor package 200 are mounted.
[0112] The semiconductor package 200 may be mounted on the circuit board 100. The semiconductor package 200 may be placed on the circuit board 100. Furthermore, the semiconductor package 200 may be connected to the circuit board 100 via conductive bumps 300.
[0113] The semiconductor package 200 may include a semiconductor chip including an integrated circuit, a semiconductor package substrate connected to the semiconductor chip, conductive solder connecting the semiconductor chip and the semiconductor package substrate, and a sealing portion sealing the semiconductor chip and the conductive solder. The sealing portion may include a resin composition such as an epoxy molding material.
[0114] The semiconductor package 200 may be a memory device, a central processing unit, or the like.
[0115] The conductive bumps 300 may be disposed between the semiconductor package 200 and the circuit board 100. Alternatively, the conductive bumps 300 may electrically connect the semiconductor package 200 and the circuit board 100. Alternatively, the conductive bumps 300 may be electrically connected to the semiconductor package 200 and a connection pad.
[0116] The heat dissipation unit 400 may be disposed on the semiconductor package 200. Alternatively, the heat dissipation unit 400 may cover the semiconductor package 200. Alternatively, the heat dissipation unit 400 may be bonded to the circuit board 100. Alternatively, the heat dissipation unit 400 may cover the side surface of the semiconductor package 200.
[0117] The heat dissipation unit 400 may include a conductor. Alternatively, the heat dissipation unit 400 may include a metal. Alternatively, the heat dissipation unit 400 may be thermally connected to an external heat dissipation fin.
[0118] Furthermore, the heat dissipation unit 400 may be capable of protecting the semiconductor package 200 from external physical impacts. Also, the heat dissipation unit 400 may be capable of protecting the semiconductor package 200 from external electromagnetic waves. That is, the heat dissipation unit 400 may be capable of blocking external electromagnetic waves.
[0119] The thermally conductive layer 500 may be disposed between the semiconductor package 200 and the heat dissipation unit 400. Alternatively, the thermally conductive layer 500 may be in direct contact with the semiconductor package 200 and the heat dissipation unit 400. Alternatively, the thermally conductive layer 500 may be in close contact with the semiconductor package 200 and the heat dissipation unit 400.
[0120] The thermally conductive layer 500 may be thermally coupled to the semiconductor package 200 and the heat dissipation unit 400. That is, the thermally conductive layer 500 may transfer heat generated from the semiconductor package 200 to the heat dissipation unit 400.
[0121] The thickness of the thermally conductive layer 500 can be from about 1 μm to about 100 μm, from about 2 μm to about 70 μm, from about 5 μm to about 60 μm, or from about 10 μm to about 40 μm.
[0122] <Method of manufacturing a semiconductor device> The method for manufacturing the semiconductor device is not particularly limited, and any known manufacturing method can be used.
[0123] First, the semiconductor package 200 may be mounted on the circuit board 100 using the conductive bumps 300. Next, a silicone-based resin composition may be applied to the semiconductor package 200. Alternatively, the silicone-based resin composition may be applied to the lower surface of the heat dissipation portion 400.
[0124] Next, the semiconductor package 200 may be covered with the heat dissipation part 400. This allows the applied silicone resin composition to come into direct contact with the lower surface of the heat dissipation part 400 and the upper surface of the semiconductor package 200, and the curable silicone resin composition can be cured at about 80°C or higher under an applied pressure of about 0.01 MPa or higher.
[0125] The pressure in the curing step may be about 0.01 MPa or more, or about 0.05 MPa to about 100 MPa, or about 0.1 MPa to about 100 MPa.
[0126] The temperature in the curing step may be about 110°C to about 300°C. The temperature in the curing step may be about 120°C to about 300°C. The temperature in the curing step may be about 140°C to about 300°C. The curing time in the curing step may be about 30 minutes to about 5 hours. By this step, the thermally conductive layer 500 can be formed.
[0127] The present invention will be described in more detail below with reference to examples and comparative examples, but the following examples and comparative examples are merely illustrative examples for explaining the present invention in more detail, and the present invention is not limited by the following examples and comparative examples. [Example]
[0128] -Organopolysiloxane #1: A compound represented by the above formula 4, having a viscosity of 20,000 cPs at 23°C and containing silicon-bonded alkenyl groups. -Organopolysiloxane #2: A compound represented by the above formula 6, having a viscosity of 1,000 cPs at 23°C and a structure in which hydrogen groups are bonded to both ends -Organopolysiloxane #3: A compound represented by the above formula 8, having a viscosity of 1,000 cPs at 23°C and a structure in which hydrogen groups are bonded to side chains. -Conductive filler #1: Tap density approximately 0.7 g / cm 3 , specific surface area is about 1.3m 2 / g, uniformity of average particle size ((D 90 -D 50 ) / (D 50 -D 10 )) is 1.1, aspect ratio is 12 (dendrite type), Ig-loss at approximately 538°C is 0.4 wt%, and silver powder surface-treated with fatty acid -Conductive filler #2: Tap density is approximately 6.4 g / cm 3 , specific surface area is about 0.3m 2 / g, uniformity of average particle size ((D 90 -D 50 ) / (D 50 -D 10)) is 1.8, aspect ratio is 1.5 (spherical), and Ig-loss is 0.05 wt% at approximately 538°C. - Tackifier: 3-glycidoxypropyltrimethoxysilane -Curing catalyst: Platinum-divinyltetramethyldisiloxane complex -Reaction inhibitor: 1-ethynyl-1-cyclohexanol
[0129] Examples 1 to 4 and Comparative Examples 1 to 4 Each of the compositions shown in Table 1 below was placed in a planetary mixer and mixed uniformly at room temperature at a speed of about 40 rpm for 1 hour to prepare a silicone resin composition.
[0130] [Table 1]
[0131] Experimental example <Sample Preparation> Each of the silicone resin compositions of Examples 1 to 4 and Comparative Examples 1 to 4 was molded into a sheet by hot pressing under the temperature, pressure, and time conditions shown in Table 2. The resulting sheet was then cured at 150°C for 2 hours, and a sample measuring 30 mm wide, 30 mm long, and 4 mm thick was then prepared.
[0132] [Table 2]
[0133] Experimental Example 1 - Thermal Conductivity Measurement The thermal conductivity of the samples prepared in Example 1-1 to Comparative Example 4-5 was measured at 25° C. using a thermal conductivity measuring device (model name: TPS-2500S, manufacturer: Hot Disk AB) according to the method of ISO22007-2. The results are shown in Table 3 below.
[0134] Experimental Example 2 - Measurement of thermal conductivity after thermal shock The samples prepared in Example 1-1 to Comparative Example 4-5 were placed in a thermal shock tester (product name: TSE-11-A) set to alternate between -40°C and 125°C for 30 minutes. After cycling through these temperatures 300 times, the thermal conductivity was measured in the same manner as in Experimental Example 1. The results are shown in Table 3 below.
[0135] Experimental Example 3 - Appearance Evaluation After repeating the test 300 times according to Experimental Example 2, the state of the samples of Example 1-1 to Comparative Example 4-5 was visually observed. A state in which no voids or cracks occurred was evaluated as ○, and a state in which voids or cracks occurred was evaluated as ×. The results are shown in Table 3 below.
[0136] [Table 3]
[0137] Tables 1 to 3 confirm that even silicone-based resin compositions with the same composition exhibit different thermal conductivity characteristics depending on the applied pressure. Specifically, Examples 1 to 4 showed no significant change in thermal conductivity regardless of the pressure applied during the sheet manufacturing process, and their thermal conductivity after thermal shock was similar to that before the thermal shock, resulting in excellent heat dissipation. Furthermore, since no voids or cracks were generated after the thermal shock, they also showed excellent durability. Furthermore, it was confirmed that Examples 1 to 4 exhibited relatively high thermal conductivity for the same conductive filler content compared to Comparative Examples 1 to 4.
[0138] In Comparative Examples 1 to 4, the rate of change in thermal conductivity due to the pressure applied in the sheet manufacturing process exceeded 30%, resulting in a large change in thermal conductivity between before and after the thermal shock. Furthermore, in Comparative Examples 1 to 4, voids and cracks occurred after the thermal shock. Therefore, it was confirmed that Comparative Examples 1 to 4 had reduced heat dissipation and durability compared to the Examples. Furthermore, it was confirmed that Comparative Examples 1 to 4 exhibited relatively low thermal conductivity compared to Examples 1 to 4 for the same conductive filler content. [Explanation of symbols]
[0139] 10: Silicone resin composition 11: First sheet 12: Second sheet 11-1: First sheet sample 12-1: Second sheet sample 20: Molding material 30: Drying oven 40: Sensor 100: Circuit board 200:Semiconductor packages 300: Conductive bump 400: Heat dissipation part 500: Heat conduction layer
Claims
1. a first conductive powder comprising dendritic particles; and A second conductive powder comprising spherical particles A conductive filler comprising: the uniformity of the average particle size of the first conductive powder calculated according to the following formula 1 is 0.3 to 4.0, [Formula 1] (D 90 -D 50 ) / (D 50 -D 10 ) In the formula, D 10 is the diameter corresponding to 10% of the cumulative volume of the first conductive powder, and D 50 is the diameter corresponding to 50% of the cumulative volume of the first conductive powder, and D 90 is a diameter corresponding to 90% of the cumulative volume of the first conductive powder.
2. organopolysiloxane, and Conductive Filler A silicone-based resin composition comprising: The rate of change in thermal conductivity measured by the following measurement method is 30% or less, [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2 The silicone resin composition was separately hot-pressed at 165°C and a pressure of 0.1 kgf / cm for 15 minutes to produce a first sheet. 2 The mixture is hot-pressed under the conditions of for 15 minutes to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO 22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (TC 26 -TC 0.1 │ / TC 26 ) x 100 In the formula, TC 26 is the thermal conductivity (W / mK) of the first sheet sample, and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample.
3. 3. The silicone resin composition according to claim 2, wherein the organic polysiloxane and the conductive filler are contained in a weight ratio of 20:80 to 5:
95.
4. 3. The silicone-based resin composition according to claim 2, wherein the conductive filler comprises a first conductive powder comprising dendritic particles and a second conductive powder comprising spherical particles.
5. 5. The silicone resin composition according to claim 4, wherein the conductive filler contains the first conductive powder and the second conductive powder in a weight ratio of 5:95 to 80:
20.
6. 5. The silicone resin composition according to claim 4, wherein the conductive filler contains the first conductive powder and the second conductive powder in a weight ratio of 5:95 to 50:
50.
7. The tap density of the first conductive powder is 0.1 g / cm 3 ~3.0 g / cm 3 5. The silicone resin composition according to claim 4, wherein
8. The specific surface area of the first conductive powder is 0.2 m 2 / g to 5.0m 2 The silicone resin composition according to claim 4, wherein the molecular weight of the silicone resin composition is 1 / g.
9. 3. The silicone resin composition according to claim 2, wherein the filler has a thermal conductivity per weight of 1 W / mK or more as calculated by the following formula 3: [Formula 3] X / Y x 10 In the formula, X is the thermal conductivity of the first sheet sample or the second sheet sample measured at 25°C, and Y is the weight percentage of the conductive filler relative to the total weight of the silicone-based resin composition.
10. 3. The silicone resin composition according to claim 2, wherein the first sheet sample or the second sheet sample has a thermal conductivity of 10 W / mK or more measured at 25°C.
11. Semiconductor packages, a heat dissipation portion disposed on the semiconductor package; and a thermally conductive layer interposed between the semiconductor package and the heat dissipation portion; A semiconductor device comprising: the thermally conductive layer contains a silicone-based resin composition, the silicone-based resin composition contains an organic polysiloxane and a conductive filler; and the rate of change in thermal conductivity of the silicone resin composition measured by the following measurement method is 30% or less, [Measurement method] 1) The silicone resin composition was heated at 165°C under a pressure of 26 kgf / cm 2 The silicone resin composition was separately hot-pressed at 165°C and a pressure of 0.1 kgf / cm for 15 minutes to produce a first sheet. 2 The mixture is hot-pressed under the conditions of for 15 minutes to produce a second sheet. 2) The first sheet and the second sheet are cured at 150° C. for 2 hours to produce a first sheet sample and a second sheet sample. 3) The thermal conductivity of the first sheet sample and the thermal conductivity of the second sheet sample are measured at 25°C in accordance with ISO 22007-2. 4) The rate of change in thermal conductivity is calculated according to the following formula 2. [Formula 2] Rate of change in thermal conductivity (%) = (TC 26 -TC 0.1 │ / TC 26 ) x 100 In the formula, TC 26 is the thermal conductivity (W / mK) of the first sheet sample, and TC 0.1 is the thermal conductivity (W / mK) of the second sheet sample.
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