Electroplating device and substrate cleaning method

Abstract

The present invention belongs to the technical field of semiconductor apparatuses. Provided are an electroplating device and a substrate cleaning method. The electroplating device comprises: a chuck for holding a substrate horizontally; a driving device for driving the chuck to rotate; and a nozzle for spraying a cleaning fluid to clean the substrate held by the chuck, wherein the coverage range of the cleaning liquid sprayed by the nozzle to the substrate includes: a forward rotating speed region and a reverse rotating speed region, the forward rotating speed region being larger than the reverse rotating speed region; and the forward rotating speed region is a region in which the cleaning fluid sprayed out from the nozzle has a velocity component along the rotating direction of the substrate, and the reverse rotating speed region is a region in which the cleaning fluid sprayed out from the nozzle has a velocity component against the rotating direction of the substrate. In the electroplating device and the substrate cleaning method of the present invention, the nozzle is positioned in a targeted manner, enabling more cleaning fluid sprayed from the nozzle to fall into the forward rotating speed region, thereby facilitating effective discharge of the cleaning fluid into a water retaining cover and preventing a large amount of cleaning liquid from falling into a cathode chamber to dilute a cathode electroplating solution and affecting the stability of the electroplating solution.

Description

Electroplating device and substrate cleaning method Technical Field

[0001] The present application relates to the field of semiconductor equipment technology, and in particular to an electroplating device and a substrate cleaning method. Background Art

[0002] With the advancement of semiconductor technology, the manufacturing of semiconductor substrates is rapidly developing towards multi-layering, stacking, functionalization, and integration. Traditional vertical electroplating processes can no longer meet the technical requirements for high-quality, high-reliability interconnect holes. Therefore, horizontal electroplating technology has emerged. It is a continuation of the development of vertical electroplating technology, that is, a new electroplating technology developed on the basis of vertical electroplating technology. In the horizontal electroplating process, the stability of the electroplating solution has a significant impact on the reliability of the electroplated product. The electroplating solution used in each electroplating process is different. To prevent cross-contamination of the electroplating solution from different electroplating processes and affect the stability of the electroplating solution, the current processing method in the market is generally to clean the substrate after each electroplating process to remove the electroplating solution carried on the substrate surface before transferring the substrate to the next electroplating process chamber.

[0003] However, when cleaning substrates using the existing method, a large amount of water falls, and some of the water falls into the cathode chamber of the electroplating device, diluting the electroplating solution in the cathode chamber and also affecting the stability of the electroplating solution. Therefore, this problem needs to be solved urgently. Summary of the Invention

[0004] In order to prevent the stability of the electroplating solution from being affected by a large amount of water falling during the substrate cleaning process, the present invention provides an electroplating device comprising:

[0005] A chuck for keeping the substrate in a horizontal position;

[0006] A driving device, used for driving the chuck to rotate;

[0007] a nozzle for spraying a cleaning liquid to clean the substrate held by the chuck;

[0008] Among them, the coverage range of the nozzle spraying the cleaning liquid onto the substrate includes: a forward rotation speed area and a reverse rotation speed area, the forward rotation speed area is larger than the reverse rotation speed area; the forward rotation speed area is an area where the cleaning liquid sprayed from the nozzle has a speed component in the direction of the substrate rotation speed; the reverse rotation speed area is an area where the cleaning liquid sprayed from the nozzle has a speed component in the direction opposite to the substrate rotation speed.

[0009] According to a specific implementation of an embodiment of the present application, the nozzle is a fan-shaped nozzle, a circular nozzle, an annular nozzle or a cylindrical nozzle.

[0010] According to a specific implementation of the embodiment of the present application, the coverage range of the cleaning liquid sprayed by the nozzle includes the center of the substrate held by the chuck.

[0011] According to a specific implementation method of an embodiment of the present application, when the cleaning liquid sprayed from the nozzle contacts the substrate, the distance between the boundary of the cleaning liquid in the forward rotation speed area and the center of the substrate is greater than or equal to r / 2, where r is the distance between the center of the substrate and the edge of the substrate.

[0012] According to a specific implementation of the embodiment of the present application, the cleaning liquid sprayed by the nozzle is located at a distance from the boundary of the reverse speed region to the center of the substrate that is less than or equal to r / 4.

[0013] According to a specific implementation of the embodiment of the present application, the driving device drives the chuck to rotate at a speed greater than or equal to 50 r / min.

[0014] According to a specific implementation of the embodiment of the present application, the flow rate of the cleaning liquid sprayed out by the nozzle is 0.5-2.5LPM.

[0015] In a second aspect, the present invention provides a substrate cleaning method, comprising:

[0016] The chuck keeps the substrate in a horizontal setting;

[0017] The driving device drives the chuck to rotate;

[0018] The nozzle sprays cleaning liquid onto the substrate to clean the substrate held by the chuck, and the coverage range of the nozzle spraying the cleaning liquid onto the substrate includes: a forward rotation speed area and a reverse rotation speed area, wherein the forward rotation speed area is larger than the reverse rotation speed area; the forward rotation speed area is an area where the cleaning liquid sprayed from the nozzle has a speed component in the direction of the substrate rotation speed; the reverse rotation speed area is an area where the cleaning liquid sprayed from the nozzle has a speed component in the direction opposite to the substrate rotation speed.

[0019] According to a specific implementation of an embodiment of the present application, the nozzle is a fan-shaped nozzle, a circular nozzle, an annular nozzle or a cylindrical nozzle.

[0020] According to a specific implementation of the embodiment of the present application, the coverage range of the cleaning liquid sprayed by the nozzle includes the center of the substrate held by the chuck.

[0021] According to a specific implementation method of an embodiment of the present application, when the cleaning liquid sprayed from the nozzle contacts the substrate, the distance between the boundary of the cleaning liquid in the forward rotation speed area and the center of the substrate is greater than or equal to r / 2, where r is the distance between the center of the substrate and the edge of the substrate.

[0022] According to a specific implementation of the embodiment of the present application, the cleaning liquid sprayed by the nozzle is located at a distance from the boundary of the reverse speed region to the center of the substrate that is less than or equal to r / 4.

[0023] The electroplating device and substrate cleaning method of the present invention divide the coverage of the cleaning liquid sprayed from the nozzle into regions according to the rotation direction of the substrate and the flow rate direction of the cleaning liquid, and specifically set the position of the nozzle so that when cleaning the substrate, the cleaning liquid sprayed from the nozzle falls more in the forward rotation area, so that it can be better thrown into the water shield and then discharged, thereby effectively reducing the amount of water falling when cleaning the substrate, preventing a large amount of cleaning liquid from falling into the cathode chamber to dilute the electroplating liquid in the cathode chamber and affecting the stability of the electroplating liquid. Other features and advantages of the present invention will be explained in the subsequent description, and part of them will become apparent from the description, or be understood through the implementation of the present invention. The objects and other advantages of the present invention can be achieved and obtained through the structures indicated in the description, claims and drawings.

[0024] Summary of the Figures

[0025] The features and performance of the present application are further described by the following embodiments and accompanying drawings. In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be derived from these drawings without inventive effort.

[0026] FIG1 shows a schematic structural diagram of an electroplating device in an embodiment of the present invention;

[0027] FIG2 is a schematic diagram showing the division of the water drop area in the cathode chamber during the substrate cleaning process according to an embodiment of the present invention;

[0028] FIG3 shows the water drop results of each area in FIG2 when the central axis of the cleaning liquid sprayed from the nozzle in an embodiment of the present invention passes through the center of the substrate;

[0029] FIG4 is a schematic diagram showing a structure in which the central axis of the cleaning liquid sprayed from the nozzle passes through the center of the chuck and the substrate in an embodiment of the present invention;

[0030] FIG5 is a schematic diagram showing the flow rate of the cleaning liquid in an embodiment of the present invention;

[0031] FIG6 is a schematic diagram showing a structure in which the central axis of the cleaning liquid sprayed from the nozzle does not pass through the center of the chuck and the substrate in an embodiment of the present invention;

[0032] FIG7 shows a schematic flow chart of a substrate cleaning method according to an embodiment of the present invention; and

[0033] FIG. 8 shows the water drop results of each area in FIG. 2 when the central axis of the cleaning liquid sprayed from the nozzle in the embodiment of the present invention does not pass through the center of the substrate.

[0034] Preferred embodiment of this application

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0036] Please refer to Figure 1, Figure 1 shows a schematic diagram of the electroplating device structure in an embodiment of the present invention. As shown in Figure 1, the electroplating device includes an electroplating chamber 100, and the electroplating chamber 100 is divided into two independent chambers by a horizontally arranged ion membrane 200. One side of the ion membrane 200 is an anode chamber 300, and the other side of the ion membrane 200 is a cathode chamber 400. An anode 500 is provided inside the anode chamber 300; a water shield 600 and a chuck 700 for maintaining the horizontal arrangement of the substrate are provided at the top of the cathode chamber 400, and a driving device 800 for driving the chuck 700 to rotate. It should be understood that the driving device 800 can also be configured to drive the chuck 700 to move in the vertical direction, so as to drive the chuck into or out of the cathode chamber 400 and to maintain the chuck 700 at a target height. In the actual process, considering that each substrate that undergoes an electroplating process needs to be cleaned once, the electroplating solution remaining on the substrate is cleaned off, and the electroplating device is also provided with a nozzle 900 for cleaning the substrate. The nozzle 900 includes but is not limited to: a fan-shaped nozzle, a circular nozzle, an annular nozzle or a cylindrical nozzle. The nozzle 900 can be positioned according to the actual machine situation. In the present embodiment, the nozzle 900 is fixedly arranged on the water shield 600. When the electroplating process is completed, the driving device 800 drives the chuck 700 to keep the substrate 001 moving upward, removes the plating solution, and moves it into the water shield 600. Then the driving device 800 drives the chuck 700 to rotate to clean the substrate 001. During the cleaning process, some of the cleaning liquid will fall into the cathode chamber 400 along the path of S2, affecting the stability of the plating solution. To this end, the present application proposes a solution. With reference to Figure 5, when the nozzle 900 sprays the cleaning liquid onto the substrate 001, the coverage area of ​​the nozzle 900 spraying the cleaning liquid onto the substrate 001 includes: a forward rotation speed area 901 and a reverse rotation speed area 902, wherein the forward rotation speed area 901 is larger than the reverse rotation speed area 902. Specifically, when the cleaning liquid falls on the substrate 001, the range covered by the cleaning liquid is divided into two areas according to the flow velocity direction of the cleaning liquid. One area is the area where the cleaning liquid sprayed by the nozzle 900 has a velocity component in the direction of the substrate rotation speed, which is called the forward rotation speed area 901; the other area is the area where the cleaning liquid sprayed by the nozzle 900 has a velocity component in the direction opposite to the substrate rotation speed, which is called the reverse rotation speed area 902. In the actual process, the vicinity of the coverage range of the cleaning liquid in the forward rotation speed area 901 is also considered to be the forward rotation speed area; the vicinity of the coverage range of the cleaning liquid in the reverse rotation speed area 902 is also considered to be the reverse rotation speed area. In an embodiment of the present invention, when the nozzle 900 sprays the cleaning liquid onto the substrate 001, the forward rotation speed area 901 is required to be larger than the reverse rotation speed area 902 to reduce the amount of water falling when cleaning the substrate 001. It should be understood that in this embodiment, the cleaning liquid can be deionized water.

[0037] The present application divides the coverage area of ​​the cleaning liquid sprayed from the nozzle into areas according to the rotation direction of the substrate and the flow rate direction of the cleaning liquid, and sets the position of the nozzle in a targeted manner, so that when cleaning the substrate, the cleaning liquid sprayed from the nozzle falls more in the forward rotation area, so that it can be better thrown into the water shield and then discharged, thereby effectively reducing the amount of water falling when cleaning the substrate, preventing a large amount of cleaning liquid from falling into the cathode chamber to dilute the electroplating liquid in the cathode chamber, and affecting the stability of the electroplating liquid.

[0038] Specific analysis is as follows, in the actual process, it is found that when cleaning substrates, the stability of electroplating solution is easily affected, in order to solve this problem, the inventor of the present application has carried out an in-depth analysis of this phenomenon. It is found that when the cleaning fluid ejected by nozzle 900 contacts substrate 001, the driving device 800 drives chuck 700 and the substrate 001 held by chuck 700 to rotate, and most of the cleaning fluid is thrown into the water shield 600, and then drained away by the drain port (not shown) provided on the water shield 600, but there is still a small part of the cleaning fluid that will fall into the cathode chamber 400 below, diluting the cathode plating solution, affecting the stability of the cathode plating solution. It is further found that in the process of cleaning substrates, the amount of water falling in each area below the substrate is not uniform, for this reason the inventor of the present application has carried out regional division to the water falling area below the substrate during substrate cleaning, and the specific water falling area division schematic diagram is shown in Figure 2, the arrow on the left in Figure 2 refers to the direction of rotation of the substrate, and the arrow in the lower right corner indicates the direction of the cleaning fluid ejected by nozzle 900. As can be seen from Figure 2, A\B\C\D extend from the center of the substrate 001 from the inside to the outside in sequence. Areas A1, B1, C1, D1, A2, B2, C2, and D2 are forward rotation areas, and areas A5, B5, C5, D5, A6, B6, C6, and D6 are reverse rotation areas. The amount of water falling in each area was measured and counted under the following test conditions: the central axis of the cleaning liquid sprayed from the nozzle passed through the center of the substrate, the flow rate of the cleaning liquid was 1.5l / min, the cleaning working time was maintained at 60s, and the chuck rotation speed was 400rpm. The results are shown in Figure 3, which shows the water falling results of each area in Figure 2 when the central axis of the cleaning liquid sprayed from the nozzle passed through the center of the substrate; it can be seen from Figure 3 that when the substrate is cleaned under the above conditions, after a substrate cleaning process is completed, the average total water falling amount is 120.1ml, among which the water falling amount in the forward rotation speed area is less, while the water falling amount in the reverse rotation speed area is larger, especially the water falling amount in areas C6 and D6 is larger than that in areas C2 and D2. Considering that the reason may be that C2 and D2 are located in the cleaning liquid coverage range in the forward rotation speed area, while C6 and D6 are located in the cleaning liquid coverage range in the reverse rotation speed area.

[0039] Furthermore, the reason why the amount of water falling from C6 / D6 is large is analyzed as follows: Referring to FIG4 , during the process of cleaning the substrate, the central axis of the cleaning liquid sprayed from the nozzle 900 passes through the center of the chuck 700, and the chuck 700 overlaps with the center of the substrate 001. Therefore, the central axis of the cleaning liquid sprayed from the nozzle 900 passes through the center of the substrate 001 held by the chuck 700, that is, the cleaning liquid is symmetrically distributed on both sides of the center of the substrate 001. According to the relationship between the flow velocity direction of the cleaning liquid sprayed from the nozzle 900 and the rotational speed direction of the substrate, the range covered by the cleaning liquid is divided into a forward rotational speed region 901 and a reverse rotational speed region 902, wherein the forward rotational speed region 901 refers to the region where the flow velocity direction of the cleaning liquid sprayed from the nozzle 900 has a component in the direction of the rotational speed of the substrate; the reverse rotational speed region 902 refers to the region where the flow velocity direction of the cleaning liquid sprayed from the nozzle 900 has a component in the direction of the rotational speed of the substrate. In the example shown in FIG4 , the range covered by the forward rotational speed region 901 is equal to the range covered by the reverse rotational speed region 902. During the cleaning process, the driving device 800 drives the chuck 700 to rotate at high speed with the substrate 001 held by the chuck 700. The cleaning liquid sprayed by the nozzle 900 on the substrate 001 gradually flows to the edge of the substrate 001 due to the action of centrifugal force, and is thus thrown into the water shield 600 (as shown by the dotted arrow S1 in Figure 1). Some of the cleaning liquid does not completely flow to the edge and will fall (as shown by the dotted arrow S2 in Figure 1). Please refer to Figure 5. The main reason for the two results is that the cleaning liquid sprayed by the nozzle 900 has its own flow velocity, and the substrate has a higher rotation speed. The speeds of the two are superimposed in the forward rotation speed area, and in the reverse rotation speed area, the flow velocity of the cleaning liquid itself is opposite to the rotation speed direction of the substrate, and a collision occurs, resulting in the cleaning liquid failing to move to the edge of the substrate 001 and being thrown into the water shield 600 and falling into the electroplating chamber.

[0040] In this regard, the solution proposed in this application to improve the problem of excessive water droplets is specifically referred to in FIG6 . As shown in FIG6 , when nozzle 900 is set, nozzle 900 is offset from the center of chuck 700 so that the cleaning liquid sprayed by nozzle 900 toward substrate 001 covers a forward rotation speed region 901 and a reverse rotation speed region 902 , wherein the forward rotation speed region 901 is larger than the reverse rotation speed region 902 . In this way, when nozzle 900 sprays cleaning liquid toward substrate 001 to clean substrate 001, the area where the flow rate of the cleaning liquid and the centrifugal velocity of the substrate collide will be reduced, thereby achieving the purpose of reducing the amount of water droplets.

[0041] Furthermore, the cleaning liquid sprayed from nozzle 900 covers the center of substrate 001 held by chuck 700. When the cleaning liquid sprayed from nozzle 900 contacts the substrate, the cleaning liquid is located at a boundary 9011 of forward rotation region 901 at a distance greater than or equal to r / 2 from the center of substrate 001, and the cleaning liquid is located at a boundary 9021 of reverse rotation region 902 at a distance less than or equal to r / 4 from the center of substrate 001, where r is the distance from the center of substrate 001 to the edge of substrate 001.

[0042] Furthermore, the driving device 800 drives the chuck 700 to rotate at a speed greater than or equal to 50 r / min.

[0043] Furthermore, the flow rate of the cleaning liquid sprayed from the nozzle is 0.5-2.5 LPM.

[0044] At the same time, the applicant of the present invention also proposes a substrate cleaning method. Referring to FIG. 7 , the method includes the following steps:

[0045] Step S100: The chuck keeps the substrate horizontal;

[0046] Step S200: the driving device drives the chuck to rotate;

[0047] Step S300: The nozzle sprays cleaning liquid onto the substrate to clean the substrate held by the chuck. The coverage range of the nozzle spraying the cleaning liquid onto the substrate includes: a forward rotation speed area and a reverse rotation speed area, wherein the forward rotation speed area is larger than the reverse rotation speed area; the forward rotation speed area is an area where the cleaning liquid sprayed from the nozzle has a velocity component in the direction of the substrate rotation speed; the reverse rotation speed area is an area where the cleaning liquid sprayed from the nozzle has a velocity component in the direction opposite to the substrate rotation speed.

[0048] Furthermore, the nozzle is a fan-shaped nozzle, a circular nozzle, an annular nozzle or a cylindrical nozzle.

[0049] Furthermore, the coverage range of the cleaning liquid sprayed by the nozzle includes the center of the substrate held by the chuck. When the cleaning liquid sprayed by the nozzle contacts the substrate, the distance between the boundary of the cleaning liquid in the forward rotation speed area and the center of the substrate is greater than or equal to r / 2, and the distance between the boundary of the cleaning liquid sprayed by the nozzle in the reverse rotation speed area and the center of the substrate is less than or equal to r / 4, where r is the distance between the center of the substrate and the edge of the substrate.

[0050] For example, please refer to Figure 6, and divide the radius r of the substrate into 6 equal parts. When setting the nozzle 900, the nozzle 900 is offset relative to the center of the chuck and the substrate, so that the coverage range of the cleaning liquid sprayed by the nozzle 900 includes: a forward rotation speed area and a reverse rotation speed area, wherein the forward rotation speed area occupies 2 / 3 of the cleaning liquid coverage area. In this embodiment, the distance between the boundary of the cleaning liquid in the forward rotation speed area and the center of the substrate is 2r / 3; the reverse rotation speed area occupies 1 / 3 of the cleaning liquid coverage area. In this embodiment, the distance between the boundary of the cleaning liquid in the reverse rotation speed area and the center of the substrate is 1r / 3; similarly, when the flow rate of the cleaning liquid is 1.5l / min, cleaning working time maintained at 60s, and chuck speed of 400rpm, the water falling amount of each water falling area in Figure 2 was measured and counted, and the results are shown in Figure 8. It can be seen from Figure 8 that when cleaning the substrate under the above conditions, after one substrate cleaning process is completed, the average total water falling amount drops to 89.3ml, and the average water falling amount is reduced by 25.6%. Among them, the total water falling amount in the A6 / B6 / C6 / D6 area drops from 11.2ml to 0.6ml, and the water falling amount in the range covered by the cleaning liquid in the reverse speed area decreases particularly significantly. Therefore, this scheme has a significant effect on optimizing the reduction of water falling amount.

[0051] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An electroplating device, characterized in that: Comprising: A chuck for holding a substrate horizontally; A driving device for driving the chuck to rotate; A nozzle for ejecting a cleaning liquid to clean the substrate held by the chuck; Wherein, the coverage range of the cleaning liquid ejected by the nozzle onto the substrate includes: a forward rotation speed region and a reverse rotation speed region, and the forward rotation speed region is larger than the reverse rotation speed region; the forward rotation speed region is the region where the cleaning liquid ejected by the nozzle has a velocity component in the direction of the substrate rotation speed; the reverse rotation speed region is the region where the cleaning liquid ejected by the nozzle has a velocity component opposite to the direction of the substrate rotation speed.

2. The electroplating device according to claim 1, characterized in that: The nozzle is a fan-shaped nozzle, a circular nozzle, an annular nozzle or a cylindrical nozzle.

3. The electroplating device according to claim 1, characterized in that: The coverage range of the cleaning liquid ejected by the nozzle includes the center of the substrate held by the chuck.

4. The electroplating device according to claim 3, wherein: When the cleaning liquid ejected by the nozzle contacts the substrate, the distance from the boundary of the cleaning liquid in the forward rotation speed region to the center of the substrate is greater than or equal to r / 2, where r is the distance from the center of the substrate to the edge of the substrate.

5. The electroplating apparatus according to claim 4, wherein: The distance from the boundary of the cleaning liquid in the reverse rotation speed region ejected by the nozzle to the center of the substrate is less than or equal to r / 4.

6. The electroplating device according to claim 1, characterized in that: The rotation speed of the driving device for driving the chuck to rotate is greater than or equal to 50 r / min.

7. The electroplating device according to claim 6, characterized in that: The flow rate of the cleaning liquid ejected by the nozzle is 0.5 - 2.5 LPM.

8. A substrate cleaning method, characterized in that: Comprising: The chuck holds the substrate horizontally; The driving device drives the chuck to rotate; The nozzle ejects a cleaning liquid onto the substrate to clean the substrate held by the chuck, and the coverage range of the cleaning liquid ejected by the nozzle onto the substrate includes: a forward rotation speed region and a reverse rotation speed region, wherein the forward rotation speed region is larger than the reverse rotation speed region; The forward rotation speed region is the region where the cleaning liquid ejected by the nozzle has a velocity component in the direction of the substrate rotation speed; the reverse rotation speed region is the region where the cleaning liquid ejected by the nozzle has a velocity component opposite to the direction of the substrate rotation speed.

9. The substrate cleaning method according to claim 8, wherein: The nozzle is a fan-shaped nozzle, a circular nozzle, an annular nozzle or a cylindrical nozzle.

10. The substrate cleaning method according to claim 8, wherein: The coverage range of the cleaning liquid ejected by the nozzle includes the center of the substrate held by the chuck.

11. The substrate cleaning method according to claim 10, wherein: When the cleaning liquid ejected by the nozzle contacts the substrate, the distance from the boundary of the cleaning liquid in the forward rotation speed region to the center of the substrate is greater than or equal to r / 2, where r is the distance from the center of the substrate to the edge of the substrate.

12. The substrate cleaning method according to claim 11, wherein: The distance from the boundary of the cleaning liquid in the reverse rotation speed region ejected by the nozzle to the center of the substrate is less than or equal to r / 4.

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