Plasma-assisted coating growth method

文档序号:45028 发布日期:2021-09-28 浏览:24次 中文

阅读说明:本技术 一种等离子体辅助镀层生长方法 (Plasma-assisted coating growth method ) 是由 汪嵘 黄永海 王井彩 于 2021-05-14 设计创作,主要内容包括:本发明属于等离子体技术领域,具体的说一种等离子体辅助镀层生长方法;利用PE-ALD技术在低温下能够在对单晶硅衬底上的GAN薄膜起到促进其生长的作用,且利用PE-ALD技术,能够通过其独有的自限制反应机制实现对GAN薄膜的高均匀性、高保形性以及原子尺度厚度等方面的控制,相对于等离子体增强化学气相沉积,PE-ALD技术能够将反应物与等离子分别单独的通入腔室,并在其中发生吸附反应,从而实现对薄膜厚度的可控制性。(The invention belongs to the technical field of plasma, in particular to a plasma-assisted plating layer growth method; the PE-ALD technology can play a role in promoting the growth of the GAN film on the monocrystalline silicon substrate at low temperature, can realize the control on the aspects of high uniformity, high conformality, atomic scale thickness and the like of the GAN film through a unique self-limiting reaction mechanism, and can independently introduce reactants and plasma into a chamber respectively and perform adsorption reaction in the chamber relative to plasma enhanced chemical vapor deposition, so that the controllability of the film thickness is realized.)

1. A plasma-assisted plating layer growth method is characterized in that: the method comprises the following steps:

s1: taking a film as an example, carrying out a PE-AlD method growth test; carrying out a growth test on the GaN film, and carrying out ultrasonic cleaning on the substrate Si (100) sequentially through isopropanol, propanol, ethanol and deionized water before deposition;

s2: removing oxides on the surface of the substrate Si, washing with deionized water, and drying; removing the substrate Si surface oxide by soaking the substrate Si surface oxide in a diluted hydrofluoric acid solution (HF, 2 vol%) for 2min, and blowing N2 for blow-drying after washing;

s3: placing the substrate Si on a heating plate of a cavity, and carrying out sectional heating until the temperature in the cavity reaches the temperature required by the growth of the substrate;

s4: keeping the substrate Si at the growth temperature for more than 30min, and introducing growth formula gas into the substrate Si to promote the growth of the GaN film; by using growth recipesThe following were used: 0.01s-TMG pulse, 3 s-interaction, 50 s-purge, 30s-N2/H2Mixed plasma gas, 50 s-purge, where 3 s-interaction is to increase the residence time of the crop source within the chamber;

s5: analyzing the result of the tested GaN; a series of growth experiments were performed at 150-300 degrees Celsius to determine the growth temperature window for GAN, wherein the growth cycles of GAN were all 300 cycles, and other conditions were maintained as described above.

2. A plasma-assisted plating growth method according to claim 1, wherein: when the substrate Si is placed on the heating plate for the first time, the substrate Si needs to be preheated for more than 30min at 120 ℃, and then the substrate Si is heated to the temperature required by growth in sections.

3. A plasma-assisted plating growth method according to claim 2, wherein: the TMG has higher vapor pressure at normal temperature and is 227Torr at room temperature, so that the temperature of a crop source needs to be maintained at about-1 ℃ by adopting a self-made cooling mechanism and N is used2/H2Mixed plasma as nitrogen source, N2、H2Respectively at a flow rate of 20sccm, using a carrier gas Ar of 50sccm to mix TMG and N2/H2The mixture gas was introduced into the reaction chamber at a pressure of 0.15Torr and the RF plasma generator was powered at 250W.

4. A plasma-assisted plating growth method according to claim 3, wherein: during the test of the PE-ALD method, TMG and N2/H2 mixed plasma are alternately introduced into a chamber in a pulse mode, redundant precursor sources and products are swept out of the chamber by carrier gas in a pulse interval, in one ALD process, TMG firstly reacts and adsorbs active sites on the surface of a substrate, the reaction automatically stops after the surface is saturated, and the products and new active sites on the surface are leftSimilarly, after the N2/H2 mixed plasma pulse, a new active site is formed on the growth surface, and the film grows periodically and circularly to thicken layer by layer.

5. A plasma-assisted plating growth method according to claim 4, wherein: the cooling mechanism consists of a top cover (1), a shell (2), a sealing plate (3) and an internal cooling component (4); a first cavity (26) is formed in the shell (2); the cooling assembly (4) is arranged in a first cavity (26); the top cover (1) is connected to the top of the shell (2) in a matching manner; the sealing plate (3) is fixedly connected to the front end of the shell (2); the cooling assembly (4) consists of a gas tank (41), a cooling pipe (42), a connecting cover (43) and a front bracket (44); the front end of the gas tank (41) is connected with the middle part of the front bracket (44) through a perforation; the front bracket (44) is fixedly connected to the bottom of the shell (2); the cooling pipe (42) is sleeved on the outer side of the gas tank (41); the two ends of the cooling pipe (42) are respectively provided with a cooling pipe inlet end (421) and a cooling pipe outlet end (422); the tail end of the connecting cover (43) is connected to the side wall of the shell (2) in a penetrating way; the other end of the gas tank (41) is connected with the inside of the connecting cover (43) in a matching way.

6. A plasma-assisted plating growth method according to claim 5, wherein: the lower end of the top cover (1) is symmetrically and fixedly connected with limiting plates (11); the outer side wall of the limiting plate (11) is connected to the inner side wall of the shell (2) in a sliding mode; the front end of the shell (2) is provided with a fitting groove (22); a through hole (21) is formed in the side wall of one end of the shell (2); the inlet end (421) and the outlet end (422) of the cooling pipe are respectively connected in the through hole (21) in a perforation way; a first through groove (24) is formed in the side wall of the rear end of the shell (2); a first bearing (25) is arranged in the first penetrating groove (24); the rear end of the connecting cover (43) is connected in the first bearing (25) in a penetrating way; the side wall of the front end of the shell (2) is symmetrically and fixedly connected with a connecting base (23); a buffer block (231) is arranged on the surface of the connecting base (23); the middle part of the connecting base (23) is provided with a threaded hole (232).

7. The plasma-assisted plating growth method of claim 6, wherein: limiting grooves (33) are formed in the positions, corresponding to the connecting base (23), of the two ends of the sealing plate (3); a second through groove (31) is formed in the middle of the sealing plate (3) corresponding to the first through groove (24); a second bearing (311) is arranged inside the second penetrating groove (31); the front end of the gas tank (41) is connected in a second bearing (311) through a hole; and a threaded rod (32) is connected to the position of the front side wall of the sealing plate (3) corresponding to the threaded hole (232) in a perforation manner.

8. A plasma-assisted plating growth method according to claim 7, wherein: a second cavity (431) is formed in the connecting cover (43); the rear end of the gas tank (41) is positioned in the cavity II (431); a second connecting plate (432) is fixedly connected to the outer side of the front end of the connecting cover (43); a first connecting plate (411) is fixedly connected to the outer side of the tail end of the gas tank (41); a bolt (433) is connected between the first connecting plate (411) and the second connecting plate (432) in a perforation manner; a spring (434) is fixedly connected to the bottom of the second cavity (431); the other end of the spring (434) abuts against the end of the gas tank (41).

Technical Field

The invention belongs to the technical field of plasmas, and particularly relates to a plasma-assisted plating layer growth method.

Background

Since the 80 s, nitride semiconductor system materials, such as InN, AlN, GAN, and the like, and alloys thereof, InALGaN, have been widely used in the field of optoelectronic devices such as high saturation mobility transistors, light emitting diodes, and ultraviolet detectors.

In the process of actual production, the current deposition technology of the GAN film is generally MOCVD technology, the growth temperature of the GAN film is generally more than 1000 facility degrees, and the GAN film is incompatible with the existing complementary metal oxide semiconductor technology due to the overhigh temperature and is in the MOCVD technology; since the equilibrium vapor pressure of N in the GAN thin film is increased by high temperature, the high nitrogen vacancy concentration causes the background carrier concentration of the thin film to be higher, thereby affecting the growth of the GAN thin film.

Disclosure of Invention

In order to make up the defects of the prior art and solve the problems that the balance vapor pressure of N in the GAN film is increased due to high temperature and the background carrier concentration of the film is higher due to high nitrogen vacancy concentration, thereby influencing the growth of the GAN film, the invention provides a plasma-assisted plating layer growth method.

The technical scheme adopted by the invention for solving the technical problems is as follows: a plasma-assisted plating growth method, comprising the steps of:

s1: taking a film as an example, carrying out a PE-AlD method growth test; carrying out a growth test on the GaN film, and carrying out ultrasonic cleaning on the substrate Si (100) sequentially through isopropanol, propanol, ethanol and deionized water before deposition;

s2: removing oxides on the surface of the substrate Si, washing with deionized water, and drying; removing the substrate Si surface oxide by soaking the substrate Si surface oxide in a diluted hydrofluoric acid solution (HF, 2 vol%) for 2min, and blowing N2 for blow-drying after washing;

s3: placing the substrate Si on a heating plate of a cavity, and carrying out sectional heating until the temperature in the cavity reaches the temperature required by the growth of the substrate;

s4: keeping the substrate Si at the growth temperature for more than 30min, and introducing growth formula gas into the substrate Si to promote the growth of the GaN film; the formula for growth is as follows: 0.01s-TMG pulse, 3 s-interaction, 50 s-purge, 30s-N2/H2Mixed plasma gas, 50 s-purge, where 3 s-interaction is to increase the residence time of the crop source within the chamber;

s5: analyzing the result of the tested GaN; a series of growth experiments were performed at 150-300 degrees Celsius to determine the growth temperature window for GAN, wherein the growth cycles of GAN were all 300 cycles, and other conditions were maintained as described above.

Preferably, the substrate Si needs to be preheated for more than 30min at 120 ℃ when being placed on the heating plate for the first time, and then heated to the temperature needed by growth in a subsection mode.

Preferably, the TMG has high vapor pressure at room temperature and is 227Torr at room temperature, so that a homemade cooling mechanism is needed to maintain the temperature of the crop source at about-1 ℃ and N is used2/H2Mixed plasma as nitrogen source, N2、H2Respectively at a flow rate of 20sccm, using a carrier gas Ar of 50sccm to mix TMG and N2/H2The mixture gas was introduced into the reaction chamber at a pressure of 0.15Torr and the RF plasma generator was powered at 250W.

Preferably, during the PE-ALD method, during the experiment, TMG and N2/H2 mixed plasma are alternately introduced into the chamber in a pulse mode, redundant precursor sources and products are blown out of the chamber by carrier gas in the pulse interval, in one ALD process, TMG firstly reacts with and adsorbs active sites on the surface of the substrate, the reaction automatically stops after the surface is saturated, and the products and new surface active sites are leftSimilarly, after the N2/H2 mixed plasma pulse, a new active site is formed on the growth surface, and the film grows periodically and circularly to thicken layer by layer.

Preferably, the cooling mechanism consists of a top cover, a shell, a sealing plate and an internal cooling assembly; a first cavity is formed in the shell; the cooling assembly is arranged in the first cavity; the top cover is connected to the top of the shell in a matching manner; the sealing plate is fixedly connected to the front end of the shell; the cooling assembly consists of a gas tank, a cooling pipe, a connecting cover and a front bracket; the front end perforation of the gas tank is connected with the middle part of the front bracket; the front bracket is fixedly connected to the bottom of the shell; the cooling pipe is sleeved on the outer side of the gas tank; the two ends of the cooling pipe are respectively provided with a cooling pipe inlet end and a cooling pipe outlet end; the tail end of the connecting cover is connected to the side wall of the shell through a through hole; the other end of the gas tank is connected with the inside of the connecting cover in a matching way.

Preferably, the lower end of the top cover is symmetrically and fixedly connected with limiting plates; the outer side wall of the limiting plate is connected to the inner side wall of the shell in a sliding mode; the front end of the shell is provided with a fitting groove; a through hole is formed in the side wall of one end of the shell; the inlet end and the outlet end of the cooling pipe are respectively connected in the through hole in a perforation way; a first through groove is formed in the side wall of the rear end of the shell; a first bearing is arranged inside the first penetrating groove; the rear end of the connecting cover is connected in the first bearing through a through hole; the side wall of the front end of the shell is symmetrically and fixedly connected with a connecting base; a buffer block is arranged on the surface of the connecting base; the middle part of the connecting base is provided with a threaded hole.

Preferably, the two ends of the sealing plate are provided with limit grooves corresponding to the positions of the connecting bases; a second through groove is formed in the middle of the sealing plate corresponding to the first through groove; a second bearing is arranged inside the second penetrating groove; the front end of the gas tank is connected with a second bearing through a perforation; and a threaded rod is connected to the position of the front side wall of the sealing plate corresponding to the threaded hole in a perforation manner.

Preferably, a second cavity is formed in the connecting cover; the rear end of the gas tank is positioned in the cavity II; the outer side of the front end of the connecting cover is fixedly connected with a second connecting plate; the outer side of the tail end of the gas tank is fixedly connected with a first connecting plate; a bolt is connected between the first connecting plate and the second connecting plate through a through hole; the bottom of the second cavity is fixedly connected with a spring; the other end of the spring abuts against the tail end of the gas cylinder.

The invention has the technical effects and advantages that:

according to the plasma-assisted plating layer growth method provided by the invention, the PE-ALD technology is utilized to play a role in promoting the growth of the GAN film on the monocrystalline silicon substrate at a low temperature, the PE-ALD technology is utilized to realize the control of the GAN film on the aspects of high uniformity, high conformality, atomic scale thickness and the like through a unique self-limiting reaction mechanism, and compared with the plasma-enhanced chemical vapor deposition, the PE-ALD technology can independently introduce reactants and plasma into a cavity respectively and generate an adsorption reaction in the cavity, so that the controllability of the film thickness is realized.

Drawings

The invention will be further explained with reference to the drawings.

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a first perspective view of the cooling mechanism of the present invention;

FIG. 3 is a second perspective view of the cooling mechanism of the present invention;

FIG. 4 is a third perspective view of the cooling mechanism of the present invention;

FIG. 5 is an enlarged view taken at A of FIG. 3 according to the present invention;

FIG. 6 is a cross-sectional view of the cooling mechanism of the present invention;

FIG. 7 is a perspective view of the closure plate of the present invention;

in the figure: 1. a top cover; 11. a limiting plate; 2. a housing; 21. a through hole; 22. a fitting groove; 23. a connection base; 231. a buffer block; 232. a threaded hole; 24. a first through groove; 25. a first bearing; 26. a first cavity; 3. closing the plate; 31. a second through groove; 311. a second bearing; 32. a threaded rod; 33. a limiting groove; 4. a cooling assembly; 41. a gas tank; 411. a first connecting plate; 42. a cooling tube; 421. the inlet end of the cooling pipe; 422. the outlet end of the cooling pipe; 43. a connecting cover; 431. a cavity II; 432. a second connecting plate; 433. a bolt; 434. a spring; 44. a front bracket.

Detailed Description

In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.

As shown in fig. 1 to 7, the method for growing a plasma-assisted coating according to the present invention comprises the steps of:

s1: taking a film as an example, carrying out a PE-AlD method growth test; carrying out a growth test on the GaN film, and carrying out ultrasonic cleaning on the substrate Si (100) sequentially through isopropanol, propanol, ethanol and deionized water before deposition;

s2: removing oxides on the surface of the substrate Si, washing with deionized water, and drying; removing the substrate Si surface oxide by soaking the substrate Si surface oxide in a diluted hydrofluoric acid solution (HF, 2 vol%) for 2min, and blowing N2 for blow-drying after washing;

s3: placing the substrate Si on a heating plate of a cavity, and carrying out sectional heating until the temperature in the cavity reaches the temperature required by the growth of the substrate;

s4: keeping the substrate Si at the growth temperature for more than 30min, and introducing growth formula gas into the substrate Si to promote the growth of the GaN film; the formula for growth is as follows: 0.01s-TMG pulse, 3 s-interaction, 50 s-purge, 30s-N2/H2Mixed plasma gas, 50 s-purge, where 3 s-interaction is to increase the residence time of the crop source within the chamber;

s5: analyzing the result of the tested GaN; a series of growth experiments were performed at 150-300 degrees Celsius to determine the growth temperature window for GAN, wherein the growth cycles of GAN were all 300 cycles, and other conditions were maintained as described above.

In one embodiment of the present invention, the substrate Si is preheated at 120 degrees celsius for more than 30 minutes when it is first placed on the heating plate, and then heated in stages to the temperature required for its growth.

As an embodiment of the present invention, the TMG has a high vapor pressure at room temperature and 227Torr at room temperature, so that it is necessary to maintain the temperature of the crop source at about-1 ℃ and N as N by using a homemade cooling mechanism2/H2Mixed plasma as nitrogen source, N2、H2Respectively at a flow rate of 20sccm, using a carrier gas Ar of 50sccm to mix TMG and N2/H2The mixture gas was introduced into the reaction chamber at a pressure of 0.15Torr and the RF plasma generator was powered at 250W.

In the PE-ALD method, TMG and N2/H2 mixed plasma are alternately introduced into a chamber in a pulse mode during testing, redundant precursor sources and products are purged out of the chamber by carrier gas in pulse intervals, TMG firstly reacts with and adsorbs active sites on the surface of a substrate in an ALD process, the reaction automatically stops after the surface is saturated, and the products and new active sites on the surface are leftSimilarly, after the N2/H2 mixed plasma pulse, a new active site is formed on the growth surface, and the film grows periodically and circularly to thicken layer by layer.

As an embodiment of the present invention, the cooling mechanism is composed of a top cover 1, a housing 2, a sealing plate 3 and an internal cooling assembly 4; a first cavity 26 is formed in the shell 2; the cooling assembly 4 is arranged in the first cavity 26; the top cover 1 is connected to the top of the shell 2 in a matching manner; the closing plate 3 is fixedly connected to the front end of the shell 2; the cooling assembly 4 consists of an air tank 41, a cooling pipe 42, a connecting cover 43 and a front bracket 44; the front end of the air tank 41 is connected with the middle part of the front bracket 44 through a perforation; the front bracket 44 is fixedly connected to the bottom of the shell 2; the cooling pipe 42 is sleeved outside the gas tank 41; the two ends of the cooling pipe 42 are respectively provided with a cooling pipe inlet end 421 and a cooling pipe outlet end 422; the end of the connecting cover 43 is connected to the side wall of the shell 2 through a hole; the other end of the gas tank 41 is connected with the inside of the connecting cover 43 in a matching way;

the during operation, import through gas pitcher 41 earlier lets in TMG in the gas pitcher 41, and before letting in TMG, from cooling tube inlet end 421 lets in the coolant liquid, the coolant liquid passes through the cooling tube, spiral encircleing is in the outside of gas pitcher 41, and discharge through cooling tube outlet end 422 afterwards, in the outside of device, cooling tube inlet end 421 is equipped with external cooling cistern with one side of cooling tube outlet end 422 promptly, and cooling cistern inside is provided with the circulating pump, can let in the cooling tube with the coolant liquid circulation, thereby realize the continuous cooling to gas pitcher 41, and connect cover 43 outer end and transmission equipment rigid coupling, utilize external motor to drive to connect cover 43 and rotate, thereby drive gas pitcher 41 and rotate, can be when continuously lowering the temperature to the inside TMG of gas pitcher 41, avoid the temperature to hang down excessively, the inside TMG gas of gas pitcher 41 changes into liquid, and influence follow-up adsorption reaction to the lining bottom Si.

As an embodiment of the invention, the lower end of the top cover 1 is symmetrically and fixedly connected with limiting plates 11; the outer side wall of the limiting plate 11 is connected to the inner side wall of the shell 2 in a sliding manner; the front end of the shell 2 is provided with a fitting groove 22; a through hole 21 is formed in the side wall of one end of the shell 2; the inlet end 421 and the outlet end 422 of the cooling pipe are respectively connected in the through hole 21 in a perforation way; a first through groove 24 is formed in the side wall of the rear end of the shell 2; a first bearing 25 is arranged inside the first through groove 24; the rear end of the connecting cover 43 is connected in the first bearing 25 in a penetrating way; the side wall of the front end of the shell 2 is symmetrically and fixedly connected with a connecting base 23; a buffer block 231 is arranged on the surface of the connecting base 23; a threaded hole 232 is formed in the middle of the connecting base 23;

when the cooling device works, the top cover 1 is connected to the upper end of the shell 2 in a fit manner through the limiting plate 11 at the bottom of the top cover 1, so that the upper end of the shell 2 is sealed, two through holes 21 are formed in the side wall of the shell 2, the two through holes 21 are different in horizontal height, the inlet end 421 of the cooling pipe is connected into the high-position through hole 21 in a perforation manner, and the outlet end 422 of the corresponding cooling pipe is connected into the low-position through hole 21 in a perforation manner; thereby coolant liquid is advanced the end 421 by the cooling tube of high-order and is got into under the drive of circulating pump, and the self-adaptation flows in cooling tube 42 to discharge through cooling tube of low-order play end 422, connecting cover 43 satisfies its rotation on shell 2 through the perforation on bearing 25 No. on the lateral wall of shell 2, and utilizes linking bridge 23 and shrouding 3's agreeing with to be connected, and cooperation buffer block 231 realizes the spacing effect of buffering to shrouding 3.

As an embodiment of the present invention, the two ends of the sealing plate 3 are provided with a limiting groove 33 corresponding to the position of the connecting base 23; a second through groove 31 is formed in the middle of the sealing plate 3 corresponding to the first through groove 24; a second bearing 311 is arranged inside the second penetrating groove 31; the front end of the gas tank 41 is connected in a second bearing 311 through a hole; a threaded rod 32 is connected to the front side wall of the sealing plate 3 through a hole corresponding to the threaded hole 232;

during operation, when the closing plate 3 is engaged with the housing 2, the closing plate 3 is engaged with the engaging groove 22 at the opening at the front end of the housing 2, the limiting groove 33 on the inner wall of the closing plate 3 is engaged with the connecting base 23, and the closing plate 3 is engaged with the housing 2 and fixed by the threaded rod 32.

As an embodiment of the present invention, a second cavity 431 is opened inside the connecting cover 43; the rear end of the gas tank 41 is positioned in the cavity No. two 431; a second connecting plate 432 is fixedly connected to the outer side of the front end of the connecting cover 43; a first connecting plate 411 is fixedly connected to the outer side of the tail end of the gas tank 41; a bolt 433 is connected between the first connecting plate 411 and the second connecting plate 432 in a perforation manner; a spring 434 is fixedly connected to the bottom of the second cavity 431; the other end of the spring 434 abuts against the end of the gas tank 41;

in operation, gas pitcher 41 is when installing, connect in No. two cavities 431 in connecting cover 43 through agreeing with the end of gas pitcher 41, realize being connected connecting cover 43 and gas pitcher 41, and through the fixed connection between connecting plate 411 and No. two connecting plates 432, realize the fixed connection of gas pitcher 41 and connecting cover 43, thereby under connecting cover 43 through the drive of external drive mechanism, can indirectly drive gas pitcher 41 and rotate, thereby satisfy that gas pitcher 41 rotates at shell 2 inside, avoid the cryogenic cooling of coolant liquid to gas pitcher 41, lead to the liquefaction of TMG in the gas pitcher 41.

The working principle is as follows: firstly, introducing TMG into the gas tank 41 through an inlet of the gas tank 41, introducing cooling liquid from an inlet end 421 of the cooling pipe before introducing the TMG, wherein the cooling liquid passes through the cooling pipe 42 and spirally surrounds the outer side of the gas tank 41 and is then discharged through an outlet end 422 of the cooling pipe, an external cooling liquid tank is arranged on one side of the device, namely the inlet end 421 of the cooling pipe and the outlet end 422 of the cooling pipe, a circulating pump is arranged in the cooling liquid tank and can circularly introduce the cooling liquid into the cooling pipe 42, so that the gas tank 41 is continuously cooled, the number of the through holes 21 is two, the horizontal heights of the two through holes 21 are different, wherein the inlet end 421 of the cooling pipe is connected into the high-level through hole 21 in a perforation manner, and the corresponding outlet end 422 of the cooling pipe is connected into the low-level through hole 21 in a perforation manner; thereby the coolant liquid advances end 421 by high-order cooling tube under the drive of circulating pump and gets into, the self-adaptation flows in cooling tube 42, and discharge through low-order cooling tube play end 422, and connect cover 43 outer end and transmission equipment rigid coupling, utilize external motor to drive and connect cover 43 and rotate, thereby drive gas pitcher 41 and rotate, when can continuously cool down the inside TMG of gas pitcher 41, it is low excessively to avoid the temperature, the inside TMG gas of gas pitcher 41 changes into liquid, and influence follow-up adsorption reaction to substrate Si.

The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

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