CN109378303B - Micro-needle rib cluster array micro-channel micro-heat exchanger - Google Patents
Micro-needle rib cluster array micro-channel micro-heat exchanger Download PDFInfo
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Abstract
A micro-needle rib cluster array micro-channel micro-heat exchanger belongs to the field of reinforced heat exchange of micro-electronic technology. The device structure comprises a packaging sheet 1) and a substrate (2), wherein the packaging sheets are stacked and packaged together in sequence; the packaging sheet (1) is provided with a fluid inlet (3) and a fluid outlet (4) which are connected with an external pipeline; the front surface of the substrate is provided with a micro-needle rib cluster array micro-channel (5), an inlet liquid storage tank (6) and an outlet liquid storage tank (7). The microneedle rib cluster units in the microneedle rib cluster array are arranged in line, and the X-direction spacing L and the Y-direction spacing L b And the X direction L of the micro needle rib cluster unit structure size a And the Y direction H can be realized by an MEMS processing technology through optimal design according to actual requirements. Compared with a general micro-channel micro heat exchanger, the heat dissipation device can meet the heat dissipation of a higher-power electronic chip, has the advantages of lower wall temperature at a boiling starting point, lower flowing boiling pressure drop, higher temperature distribution uniformity on the chip and the like, and enables a high-heat-flow electronic device to realize higher-efficiency heat management.
Description
Technical Field
The invention belongs to the technical field of enhanced heat exchange, and relates to a micro-needle rib cluster array micro-channel micro-heat exchanger.
Background
With the continuous development of functional and compact microelectronic devices, advanced micro-energy sources such as concentrating solar photovoltaic panels, radars, laser weapon electromagnetic guns and the like and microelectronic systems are highly modularized and miniaturized, the number of electronic elements in a limited volume is rapidly increased, the packaging density is continuously increased, the heat flux density is continuously increased, and the problem of local overhigh temperature of the microelectronic devices is increasingly outstanding. According to incomplete statistics, 55% of the failure rate of the electronic equipment is caused by the fact that the temperature exceeds the specified value of the electronic component. The working reliability of the device is very sensitive to temperature change, and when the temperature of an electronic element is increased by 10 ℃ on the limit temperature level, the reliability is reduced by half, and the service life is also greatly reduced. The high heat generated by the electronic components is not removed in time, which can pose a great threat to device reliability and service life. There is a need to research and develop efficient heat dissipation devices to meet the heat dissipation requirements of high heat flux electronic components.
The existing microcoolers studied at home and abroad are as follows: a micro-channel heat sink, a micro-freezer, a micro-heat pipe soaking piece, an integrated micro-cooler and the like. The micro-channel heat dissipation technology is used as a device-level heat dissipation method with high heat exchange coefficient, the processing technology is mature, and the micro-channel heat dissipation technology can be directly integrated on a microelectronic element, so that the micro-channel heat dissipation technology can be widely applied to array cooling of various high-power density micro-electronic devices, the problems of temperature difference reduction, difficult temperature control and the like of high-power electronic devices are effectively solved from the aspects of thermal control and thermal management, and the service life and reliability of the micro-electronic devices are prolonged. At present, the research of micro-channel heat exchange is mainly divided into two directions of single-phase convection heat transfer and evaporation heat transfer. Compared with single-phase convection heat transfer, the micro-channel boiling heat transfer has the advantages of high heat transfer coefficient, low flow velocity of working medium, small consumption of working medium, uniform heat sink temperature distribution and the like. However, the microchannel heat exchangers currently used for boiling heat transfer have the following limitations in design: first, the large pressure drop created by small scale flow boiling; secondly, the micro-machining technology leads to smooth channel wall surface, even in nano-scale roughness, and less nucleation cavities with proper size lead to higher boiling starting point and low critical heat flow density; third, boiling instability is more likely to occur.
Most of the research in the current literature focused on improvements in microchannel floors such as etched cavities, covered nanowires/carbon nanotubes, hydrophilic coatings, and rib walls such as etched cavities, diverging microchannels, sinusoidal microchannels, intermittent microchannels, by reducing boiling initiation points and enhancing heat transfer. The above method can also suppress boiling instability to some extent. In terms of controlling boiling instability, most studies in the literature choose to add a throttling device to the inlet of the microchannel to suppress flow boiling instability at the expense of increasing inlet-outlet pressure drop to consume more pumping power.
The micro-needle rib cluster array micro-channel heat exchanger is adopted, and through the optimized design of the arrangement and the size of the micro-needle rib clusters and the optimized design of the size of the micro-needle rib cluster array structure, under the condition of meeting the condition of reducing the flow resistance, the boiling starting point is reduced, the critical heat flow density is high, the heat transfer is enhanced, and the unstable boiling is thoroughly eliminated. The heat-dissipating device is applied to a high-power chip heat-dissipating device, and has the advantages of excellent heat matching performance, high-efficiency heat removal, uniform temperature and the like.
Disclosure of Invention
In view of the above, the primary technical problem to be solved by the present invention is to provide a micro-needle rib cluster array micro-channel heat exchanger, which can simultaneously achieve the effects of reducing flow resistance, reducing boiling starting point, enhancing heat transfer, eliminating boiling instability, solving the problems of high-efficiency heat removal on the surface of a microelectronic device, uniformity of chip temperature distribution, heat matching between a micro-channel evaporator and a chip, and the like, and providing reliable heat management for high-efficiency stable operation of the chip.
The invention designs a micro-needle rib cluster array micro-channel micro-heat exchanger for fluid boiling heat transfer, which is characterized by comprising a packaging sheet (1) and a substrate (2) which are sequentially stacked and packaged together as shown in figure 1; the packaging sheet (1) is provided with a fluid inlet (3) and a fluid outlet (4) which are connected with an external pipeline; the micro-needle rib cluster array micro-channel (5), an inlet liquid storage tank (6) and an outlet liquid storage tank (7) are processed on the front surface of the substrate, the inlet liquid storage tank (6) and the outlet liquid storage tank (7) are respectively positioned on two sides of the micro-needle rib cluster array micro-channel (5), the fluid inlet (3) and the inlet liquid storage tank (6) are opposite up and down, and the fluid outlet (4) and the outlet liquid storage tank (7) are opposite up and down;
as shown in fig. 2, the encapsulation sheet (1) and the substrate (2) are bonded together to form the closed micro-needle rib cluster array micro-channel heat exchanger (8). A fluid flow circuit is formed within the micro heat exchanger. In the miniature heat exchanger, working medium flows through a fluid inlet (3), an inlet liquid storage tank (6), a micro-needle rib cluster array micro-channel (5), an outlet liquid storage tank (7) and a fluid outlet (4) in sequence. After flowing through the inlet liquid storage tank (6), the heat exchange working medium is uniformly dispersed into the micro-needle rib cluster array micro-channel (5), takes heat away from the bottom surface of the micro-channel and the surface of the micro-needle rib through boiling heat transfer, and then is collected into the outlet liquid storage tank (7).
The processing area of the microneedle rib cluster array micro-channel (5) can be determined according to the size of a cooled electronic device. In order to more clearly define the structure of the substrate (2), fig. 1 (B), 1 (c), 1 (d), and 1 (e) show a top view, a front view, a cross-sectional view of the substrate (2), and a cross-sectional view of B-B, respectively.
The microneedle rib cluster array micro-channel (5) is formed by arranging or staggering a plurality of (not less than 3) microneedle rib cluster units (10) in sequence; each microneedle rib cluster unit (10) is formed by arranging a plurality of (at least three) independent microneedle rib columns, wherein the arrangement shape is selected from a circle, a diamond, a triangle, a rectangle, a water drop shape, an airfoil shape, an ellipse shape and a cone shape; the microneedle rib column arrangement density in the microneedle rib cluster unit (10) is uniform or the interior is relatively dense, the exterior is relatively thin, and the interior is dense and the exterior is thin; preferably, the distance between two adjacent microneedle rib columns with a dense inner part and a thin outer part is lc, the distance between two adjacent microneedle rib columns with a thin outer part is ls, lc is smaller than ls, and the directions of ls and lc are consistent; the arrangement mode of the microneedle rib columns of the inner denser part is the same as or different from the arrangement mode of the microneedle rib columns of the outer thinner part, for example, the inner part is arranged in the positive direction, and the outer part is arranged in a triangle. The spacing l between every two adjacent microneedle rib columns is 3-50 μm. The axial cross section shape of the single microneedle rib is selected from the group consisting of a circle, a diamond, a triangle, a rectangle, a water drop shape, an airfoil, an ellipse and a cone, and the hydraulic diameter d is 3 mu m-50 mu m.
The nearest connection direction along the inlet liquid storage pool (6) and the outlet liquid storage pool (7) in the microneedle rib cluster array micro-channel (5) is recorded as the arrangement direction of one row, the distance L between two adjacent microneedle rib cluster units (10) in one row is equal, and the distance Lb between any two rows is also equal; the microneedle rib cluster unit (10) has a dimension La in the row direction, a dimension H in the vertical row direction, and a proportional relationship between the area of the inner denser portion and the area of the outer less dense portion, and can be adjusted as required.
The middle position of the front surface of the substrate is provided with a groove, and the micro-needle rib cluster array micro-channel (5), the inlet liquid storage tank (6) and the outlet liquid storage tank (7) are all positioned in the groove. The cross section of the grooves in the vertical row direction is rectangular with equal cross section, trapezoidal with equal cross section, rectangular with variable cross section and trapezoidal with variable cross section.
The invention adopts the following technical scheme:
the invention is based on the following three mechanisms: the micro rib column increases the heat exchange area and forms a turbulent convection heat exchange theory to fluid, the gaps between adjacent micro rib columns can provide a large number of nucleation theory of nucleation holes with proper size, fluid interconnection and intercommunication among micro needle rib cluster units and fluid mechanics theory coupling two-phase flow theory of capillary force transportation in the micro needle rib cluster units for providing liquid required by nucleation and avoiding local evaporation. The micro-needle rib cluster array micro-channel (5) is adopted in the main part of the heat exchanger. As shown in FIG. 4, the micro-needle rib cluster array micro-channel (5) is formed by arranging N identical micro-needle rib clusters in sequence or staggered manner, and the flowing direction dimension L of the outermost edge point of each adjacent micro-needle rib cluster unit a And a dimension L perpendicular to the flow direction b The spacing distances are respectively equal. L (L) a And L b Size, structural shape of microneedle rib cluster unit, structural dimension flow direction dimension L and perpendicular to flow direction dimension H, manner of dense arrangement of microneedle rib columns in microneedle rib cluster unit (minimum spacing L c And maximum distance l s Size), and the cross-sectional shape and diameter d of the micro-rib column can be optimally designed according to actual requirements such as actual heat dissipation power, device size and the like. The microneedle rib clusters increase heat exchange area and disturb fluid formation, heat exchange efficiency is improved, extra nucleation cavities provided by the gaps of the microneedle rib clusters greatly reduce boiling starting points, unstable boiling caused by vapor explosion growth due to overhigh wall temperature is avoided, the existence of the gaps of the microneedle rib cluster units can enable the interior of the microchannels to form an interconnection whole, vapor-liquid two-phase boiling uniformity in the microchannels is greatly improved, temperature distribution uniformity in the microchannels is improved, capillary force transportation of liquid is enhanced by the gaps in the microneedle rib cluster units, and therefore local drying phenomenon is effectively avoided, and critical heat flow density is improved. In conclusion, the micro-needle rib cluster array micro-channel micro-heat exchanger triggered by the three-mechanism coupling effect is an extremely effective method for efficiently managing heat of a high-heat-flux chip.
The heat exchange working medium can be selected from insulating fluids such as deionized water, acetone, methanol, refrigerant (such as FC-72) and the like. According to the optimal working temperature range of the working medium and the electronic device, the micro-needle rib cluster array micro-channel evaporation heat transfer is formed on the heat exchange surface to realize the cooling technical requirement.
The material of the miniature heat exchanger can be tungsten copper, oxygen-free copper, silicon and the like. The overall geometry, dimensions may be determined based on the electronic device dimensions and overall packaging requirements. The cooling device is mainly suitable for cooling heating surfaces such as bars, squares and the like.
The invention has the advantages that:
1. the micro-needle rib cluster array micro-channel effectively increases the heat exchange area, strengthens the fluid disturbance and effectively improves the heat exchange efficiency;
2. the micro rib column gaps can be used as extra nucleation holes, so that the boiling starting point is greatly reduced, explosive growth of the nucleation bubbles with too high wall temperature under high heat flux density is avoided, and the unstable flow boiling is fundamentally eliminated;
3. compared with a micro-channel heat exchanger with common rib wall intervals, the existence of the micro-needle rib cluster unit intervals can enable the micro-channels to form an interconnection and intercommunication whole, the pressure drop is obviously reduced under the same heat exchange quantity, and the vapor-liquid two-phase boiling uniformity in the micro-channels is obviously improved, so that the temperature distribution uniformity in the micro-channels is improved;
4. compared with a micro-channel heat exchanger with common rib wall intervals, the micro-needle rib cluster unit inner gap strengthens the transportation of capillary force to liquid, thereby effectively avoiding the phenomenon of local evaporation and improving the critical heat flow density.
Drawings
Fig. 1: the invention discloses a structural schematic diagram of a micro-channel heat exchanger with a micro-needle rib cluster array;
(a) The method comprises the following steps A top view of the package sheet of the present invention;
(b) The method comprises the following steps The invention relates to a top view of a substrate with micro-cluster array micro-channels;
(c) The method comprises the following steps The invention provides a front view of a substrate with micro-needle rib cluster array micro-channels.
(d) The method comprises the following steps The invention relates to a cross-section view of a substrate A-A with micro-needle rib cluster array micro-channels.
(e) The method comprises the following steps The invention relates to a substrate B-B section view with micro-needle rib cluster array micro-channels.
Fig. 2: the present invention is schematically shown in the structure of fig. 1.
Fig. 3: the invention has the whole structure schematic diagram of the micro-needle rib cluster array micro-channel fluid cooling high-power chip micro heat exchanger;
fig. 4: the micro-needle rib cluster array micro-channel structure of the embodiment 1 of the invention is schematically shown;
(a) The method comprises the following steps A microneedle rib cluster array schematic;
(b) The method comprises the following steps The microneedle rib cluster unit structure is schematically shown.
Fig. 5: the micro-needle rib cluster array micro-channel structure of the embodiment 2 of the invention is schematically shown;
(a) The method comprises the following steps A microneedle rib cluster array schematic;
(b) The method comprises the following steps The microneedle rib cluster unit structure is schematically shown.
In the figure: 1. the micro-needle rib cluster packaging structure comprises a packaging sheet, 2, a substrate, 3, a fluid inlet, 4, a fluid outlet, 5, micro-needle rib cluster array micro-channels, 6, an inlet liquid storage pool, 7, an outlet liquid storage pool, 8, a micro heat exchanger, 9, a simulated heat source, 10 and a micro-needle rib cluster unit.
Detailed Description
A micro-pin rib cluster array micro-channel micro-heat exchanger for evaporative heat exchange is provided herein, and a preferred example of the invention is further described below with reference to the accompanying drawings and detailed description: it should be understood that the preferred examples are illustrative of the present invention and are not intended to limit the scope of the present invention.
Example 1
The micro-needle rib cluster array micro-channel micro-heat exchanger consists of a packaging sheet 1 and a micro-channel substrate 2. The packaging sheet adopts 7740 heat-resistant glass, the substrate adopts silicon, and the working medium adopts acetone. Because the cost of the high-power chip is very high, the embodiment adopts an analog heat source to replace the chip for performance test experiment research. The simulated heat source adopts a Pt platinum metal serpentine heating film. Through design optimization, the heating film can uniformly generate heat and simulate the heat generation of a high-power chip. The input voltage of the platinum heating film can be determined according to the heat generation amount of the chip.
As shown in FIG. 3, a silicon substrate was coated with a uniform snake having a thickness of 100 nm on the back surface by a plating techniqueAnd (3) forming a Pt platinum metal film, simulating the heat generation of the chip after the power is on, and cooling the heating film 9 by using a microneedle rib cluster array micro-channel heat exchanger. Micro channels with the depth of 80 microns are etched on silicon base with the thickness of 400 microns through MEMS technology, and then bonded with glass with circular fluid inlets and outlets with the diameter of 1mm, so that the miniature heat exchanger is formed. The size of the micro-channel structure area containing the micro-needle rib cluster array on the silicon substrate is consistent with that of the heating film area. The overall dimension of the whole miniature heat exchanger is 24 multiplied by 8.4 multiplied by 0.8mm 3 . The local structure of the microneedle rib cluster array is shown in fig. 4b (the inside is square arrangement, namely, the parallel arrangement, the outside is triangular arrangement, namely, the staggered arrangement), and the micro channel is formed by staggered arrangement of micro cylinder cluster units which are arranged at equal intervals (see fig. 4 a), and the flow direction and the direction perpendicular to the flow direction are defined as an X direction (namely, the row direction) and a Y direction respectively. X-direction pitch L and Y-direction pitch L b All 250 mu m, and the X-direction dimension L of the microneedle rib cluster unit a And Y-direction dimension H were 250 μm. The microneedle rib cluster unit consists of 125 microcolumns with the diameter d of 10 mu m, and forms 6 layers of inner-layer dense and outer-sparse equilateral rhombus outline, 4 layers of dense arrangement are arranged from the center to the outside, 2 layers of sparse arrangement are arranged in a dense way, and the dense arrangement is parallel to the adjacent microcolumn spacing l on the side of the rhombus outline c 4.1 μm, the spacing l between adjacent micro-cylinders parallel to the diamond outline at the sparse arrangement s 18.3 μm. The cooling working medium enters an inlet liquid storage tank 6 through a fluid inlet 3, is uniformly dispersed into micro-cylindrical diamond-shaped arranged micro-channels 5, takes heat away from the bottom surfaces of the micro-channels and the surfaces of the micro-cylinders through boiling heat transfer, is collected into an outlet liquid storage tank 7, and finally flows out from a fluid outlet 4. The uniform heat dissipation of the high heat flux electronic device is realized, the temperature of the electronic device is ensured to be maintained in the optimal working temperature range, and the service life of the electronic device is prolonged.
Example 2
The micro-needle rib cluster array micro-channel micro-heat exchanger consists of a packaging sheet 1 and a micro-channel substrate 2. The packaging sheet adopts 7740 heat-resistant glass, the substrate adopts silicon, and the working medium adopts acetone. Because the cost of the high-power chip is very high, the embodiment adopts an analog heat source to replace the chip for performance test experiment research. The simulated heat source adopts a Pt platinum metal serpentine heating film. Through design optimization, the heating film can uniformly generate heat and simulate the heat generation of a high-power chip. The input voltage of the platinum heating film can be determined according to the heat generation amount of the chip.
As shown in fig. 3, a uniform serpentine Pt platinum metal film with a thickness of 100 nm is plated on the back surface of the silicon substrate by a plating technique, and after the power is turned on, the heat generation of the chip is simulated, and the heating film 9 is cooled by a micro-needle rib cluster array micro-channel heat exchanger. Micro channels with the depth of 80 mu m are etched on silicon base with the thickness of 400 mu m through MEMS technology, and then are bonded with glass with circular fluid inlets and outlets with the diameter of 1mm, so that the micro heat exchanger is formed. The size of the micro-channel structure area containing the micro-needle rib cluster array on the silicon substrate is consistent with that of the heating film area. The overall dimension of the whole miniature heat exchanger is 24 multiplied by 8.4 multiplied by 0.8mm 3 . As shown in FIG. 5, the micro-needle rib cluster array has a local structure, and the micro-channels are composed of micro-cylinder cluster units arranged at equal intervals, wherein the distance L in the X direction (i.e. the row direction) and the distance L in the Y direction b All 170 mu m, and the X-direction dimension L of the microneedle rib cluster units a And Y-direction dimension H were 170 μm. The microneedle rib cluster unit consists of 53 microcolumns with the diameter d of 10 mu m, wherein the microcolumns form an inner-4-layer dense outer-sparse equilateral rhombus outline, 2 layers of the microcolumns are densely arranged from the center to the outside, 2 layers of the microcolumns are sparsely arranged, and the dense arrangement is parallel to the adjacent microcolumn spacing l on the side of the rhombus outline c 4.1 μm, the spacing l between adjacent micro-cylinders parallel to the diamond outline at the sparse arrangement s 18.3 μm. The cooling working medium enters an inlet liquid storage tank 6 through a fluid inlet 3, is uniformly dispersed into micro-cylindrical diamond-shaped arranged micro-channels 5, takes heat away from the bottom surfaces of the micro-channels and the surfaces of the micro-cylinders through boiling heat transfer, is collected into an outlet liquid storage tank 7, and finally flows out from a fluid outlet 4. The uniform heat dissipation of the high heat flux electronic device is realized, the temperature of the electronic device is ensured to be maintained in the optimal working temperature range, and the service life of the electronic device is prolonged.
This example differs from example 1 only in the structure of the micro pin rib cluster array micro channels. First, in example 1, the microneedle rib cluster units are arranged in a row, and in example 1, the microneedle rib cluster units are arranged in a staggered row, with an X-direction pitch L and a Y-direction pitch L b Are smaller than the corresponding dimensions in example 1; next, the number of micro-cylinders in the micro-needle rib cluster unit in example 2 is smaller than that in example 1So that the number of layers from the center to the outside is smaller than that in the embodiment 1, and the X-direction dimension L of the microneedle rib cluster unit a And Y-direction dimension H are smaller than the corresponding dimensions in example 1.
Claims (6)
1. The micro-needle rib cluster array micro-channel micro-heat exchanger is characterized by comprising a packaging sheet (1) and a substrate (2) which are sequentially stacked and packaged together; the packaging sheet (1) is provided with a fluid inlet (3) and a fluid outlet (4) which are connected with an external pipeline; the micro-needle rib cluster array micro-channel (5), an inlet liquid storage tank (6) and an outlet liquid storage tank (7) are processed on the front surface of the substrate, the inlet liquid storage tank (6) and the outlet liquid storage tank (7) are respectively positioned on two sides of the micro-needle rib cluster array micro-channel (5), the fluid inlet (3) and the inlet liquid storage tank (6) are opposite up and down, and the fluid outlet (4) and the outlet liquid storage tank (7) are opposite up and down;
the microneedle rib cluster array micro-channel (5) is formed by arranging a plurality of microneedle rib cluster units (10) in sequence or staggering; each of which is provided with
The microneedle rib cluster unit (10) is formed by arranging a plurality of independent microneedle rib columns;
the microneedle rib column arrangement density in the microneedle rib cluster unit (10) is uniform or the interior is relatively dense, the exterior is relatively thin, and the interior is dense and the exterior is thin; the distance between two adjacent microneedle rib columns with a dense inner part and a dense outer part is lc, the distance between two adjacent microneedle rib columns with a thin outer part is ls, lc is smaller than ls, and the directions of ls and lc are consistent; the arrangement mode of the microneedle rib columns with the dense inner part is the same as or different from that of the microneedle rib columns with the thin outer part;
the microneedle rib cluster array micro-channel (5) is formed by arranging no less than 3 microneedle rib cluster units (10) in sequence or staggered manner; each microneedle rib cluster unit (10) is formed by arranging at least three independent microneedle rib columns, wherein the arrangement shape is selected from one of round, diamond, triangle, rectangle, drop-shaped, airfoil, ellipse and cone.
2. A micro-needle rib cluster array micro-channel micro-heat exchanger according to claim 1, wherein the distance l between two adjacent micro-needle rib columns is 3 μm-50 μm.
3. The micro-channel micro heat exchanger of the micro-needle rib cluster array according to claim 1, wherein the axial cross section shape of the single micro-needle rib column is selected from one of a circle, a diamond, a triangle, a rectangle, a drop shape, an airfoil shape, an ellipse and a cone shape, and the hydraulic diameter d is 3 μm-50 μm.
4. A micro-channel micro-heat exchanger according to claim 1, wherein the nearest connection direction of the inlet liquid storage tank (6) and the outlet liquid storage tank (7) in the micro-pin rib cluster array micro-channel (5) is marked as an arrangement direction of one row, the distance L between two adjacent micro-pin rib cluster units (10) in one row is equal, and the distance Lb between any two rows is also equal.
5. The micro-needle rib cluster array micro-channel micro-heat exchanger according to claim 1, wherein a groove is arranged in the middle of the front surface of the substrate, and the micro-needle rib cluster array micro-channel (5), the inlet liquid storage tank (6) and the outlet liquid storage tank (7) are all positioned in the groove; the cross section of the grooves in the vertical row direction is one of a constant cross section rectangle, a constant cross section trapezoid, a variable cross section rectangle and a variable cross section trapezoid.
6. The micro-needle rib cluster array micro-channel micro-heat exchanger according to claim 1, wherein the substrate and the packaging sheet are made of the following materials: one of tungsten copper, oxygen-free copper and silicon; the height of the micro needle rib cluster array micro channel (5) is larger than the thickness of the substrate.
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