Base temperature detection method for semiconductor equipment

Abstract

The invention discloses a base temperature detection method for semiconductor equipment. The base temperature detection method comprises the steps that S1, each rotation period of a base is divided into a plurality of detection intervals in sequence; the plurality of detection intervals comprise an abnormal detection interval in which a detection light path of a pyrometer for detecting the center temperature of the base is shielded by the bracket and a normal detection interval in which the detection light path of the pyrometer is not shielded by the bracket; and S2, when the current detection interval is the abnormal detection interval, predicting the temperature prediction value of the current detection interval based on the effective temperature values of N detection intervals before the current detection interval, and taking the temperature prediction value as the effective temperature value of the current detection interval, wherein N is greater than or equal to 2.

Description

Technical Field

[0001] This invention relates to the field of semiconductor equipment technology, and in particular to a method for detecting the base temperature of semiconductor equipment. Background Technology

[0002] In semiconductor manufacturing, the substrate used to support the wafer within the reaction chamber is typically mounted on a support frame, which further drives the rotation of both the substrate and the wafer. During this process, a pyrometer positioned at the bottom of the reaction chamber measures the temperature of the back of the substrate. Since the pyrometer detects the temperature of the back of the substrate by emitting a detection light path, and because the pyrometer emits the light at a fixed angle, parts of the support frame can obstruct this light path during rotation. Furthermore, the temperature difference between the support frame and the back of the substrate can affect the accuracy of the pyrometer's temperature measurement.

[0003] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Summary of the Invention

[0004] The purpose of this invention is to provide a method for detecting the base temperature of semiconductor devices, so as to solve the problem of temperature measurement error caused by the bracket blocking the detection optical path of the pyrometer and the temperature difference between the bracket and the back of the base during the base rotation process.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] This invention provides a method for detecting the base temperature of a semiconductor device, comprising:

[0007] Step S1: Divide each rotation cycle of the base into multiple detection intervals in sequence; the multiple detection intervals include an abnormal detection interval where the detection optical path of the pyrometer used to detect the temperature on the back of the base is blocked by the bracket and a normal detection interval where the detection optical path of the pyrometer is not blocked by the bracket.

[0008] Step S2: When the current detection interval is an abnormal detection interval, the temperature prediction value of the current detection interval is predicted based on the effective temperature values ​​of the previous N detection intervals, and the predicted temperature value is used as the effective temperature value of the current detection interval; where N≥2.

[0009] Optionally, in step S2, when the current detection interval is a normal detection interval, the temperature detection value of the pyrometer in the current detection interval is taken as the effective temperature value of the current detection interval.

[0010] Optionally, in step S2, when the difference between the temperature detection value of the current detection interval and the effective temperature value of the previous detection interval is less than or equal to a preset threshold, the current detection interval is determined to be a normal detection interval.

[0011] If the difference between the temperature value detected in the current detection interval and the effective temperature value in the previous detection interval is greater than a preset threshold, the current detection interval is determined to be an abnormal detection interval.

[0012] Optionally, the semiconductor device further includes a heating component, and the base temperature detection method further includes: adjusting the heating power of the heating component based on the obtained effective temperature value.

[0013] Optionally, step S1 includes: when dividing each rotation cycle of the base into multiple detection intervals, numbering each detection interval sequentially;

[0014] In step S2, the step of predicting the temperature prediction value of the current detection interval based on the effective temperature values ​​of the previous N detection intervals includes: constructing a linear regression model based on the effective temperature values ​​and numbers of the N detection intervals, and inputting the number of the current detection interval into the linear regression model to obtain the temperature prediction value of the current detection interval.

[0015] Optionally, in step S2, when the current detection interval is an abnormal detection interval and the previous detection interval is a normal detection interval, the N detection intervals include at least two normal detection intervals between the current detection interval and the previous abnormal detection interval.

[0016] Optionally, in step S2, when the current detection interval is an abnormal detection interval and the previous detection interval of the current detection interval is an abnormal detection interval, the N detection intervals include: the previous detection interval; and all detection intervals used to predict the effective temperature value of the previous detection interval.

[0017] Optionally, the bracket includes a rotating shaft and multiple support arms. The base is connected to the rotating shaft via the multiple support arms that are evenly distributed circumferentially. The rotating shaft drives the base to rotate via the multiple support arms. During one rotation cycle of the base, the multiple support arms sequentially block the detection optical path of the pyrometer to form multiple abnormal detection intervals.

[0018] Optionally, in step S2, when the current detection interval is an abnormal detection interval blocked by a support arm, the N detection intervals include: all normal detection intervals between the current detection interval and the abnormal detection interval blocked by the previous support arm during the rotation of the base.

[0019] Optionally, in each detection interval, the pyrometer collects multiple raw temperature values ​​at fixed time intervals, and the average of the multiple raw temperature values ​​is used as the temperature detection value.

[0020] Optionally, step S1 includes: dividing each rotation cycle of the base into multiple detection intervals of equal duration.

[0021] This invention has at least the following technical effects:

[0022] When an abnormal detection zone occurs where the detection optical path of the pyrometer is blocked by the bracket, the temperature value of the abnormal detection zone can be predicted based on the effective temperature values ​​of multiple detection zones preceding the abnormal detection zone. This can avoid environmental errors in the abnormal detection zone, reduce temperature fluctuations, and improve the accuracy of temperature detection. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the cavity structure of a semiconductor device.

[0024] Figure 2 for Figure 1 Enlarged schematic diagram of the structure at the central support;

[0025] Figure 3 A schematic diagram showing how the support arm blocks the detection optical path of the lower pyrometer;

[0026] Figure 4 This is a real-time temperature curve of the pyrometer when abnormal temperature detection values ​​collected during shading are not processed.

[0027] Figure 5 This is a comparison diagram showing the effect before and after using the base temperature detection method of the present invention;

[0028] Figure 6 A flowchart of a method for detecting the base temperature of a semiconductor device according to an embodiment of the present invention;

[0029] Figure 7 This is a schematic diagram illustrating how each rotation cycle of the base is sequentially divided into multiple detection intervals, according to an embodiment of the present invention.

[0030] Explanation of reference numerals in the attached figures:

[0031] 100: Semiconductor equipment; 110: Cavity;

[0032] 111: Internal volume; 112: Upper dome;

[0033] 113: Upper lining; 114: Lower dome;

[0034] 115: Lower lining; 120: Base;

[0035] 121: Wafer; 122: Scaffold;

[0036] 123: Rotation axis; 124: Support arm;

[0037] 125: Mounting hole; 126: Through hole;

[0038] 130: Air inlet; 131: Air outlet;

[0039] 140: Heating component; 141: Lamp assembly;

[0040] 143: Upper headlight assembly; 144: Lower headlight assembly;

[0041] 151: Upper pyrometer; 152: Lower pyrometer;

[0042] 161: Lifting pin; 162: Lifting shaft;

[0043] 163: Limiting part; 164: Lifting arm;

[0044] RA: Rotation axis Detailed Implementation

[0045] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the base temperature detection method for semiconductor devices proposed by the present invention. The advantages and features of the present invention will become clearer from the following description. It should be noted that the accompanying drawings are in a very simplified form and use non-precise proportions, used only to facilitate and clearly illustrate the embodiments of the present invention. Please refer to the accompanying drawings to make the objectives, features, and advantages of the present invention more apparent and understandable. It should be understood that the structures, proportions, sizes, etc., depicted in the accompanying drawings are only for illustrative purposes to aid those skilled in the art and are not intended to limit the implementation conditions of the present invention. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to the size, without affecting the effects and objectives achieved by the present invention, should still fall within the scope of the technical content disclosed in the present invention.

[0046] like Figure 1As shown, the semiconductor device 100 includes a cavity 110, a base 120, and a heating assembly 140. The cavity 110 is, for example, an epitaxial cavity. The cavity 110 mainly includes an upper dome 112, an upper liner 113, a lower dome 114, and a lower liner 115. The upper dome 112 and the lower dome 114 are, for example, made of transparent quartz material, while the upper liner 113 and the lower liner 115 are, for example, made of opaque quartz material. The upper dome 112, the upper liner 113, the lower dome 114, and the lower liner 115 together define the internal volume 111 of the cavity 110. A base 120 for supporting and rotating a wafer 121 is disposed in the internal volume 111. The base 120 is, for example, made of ceramic, silicon carbide, or silicon carbide-coated graphite.

[0047] like Figure 1 As shown, the semiconductor device 100 also includes an inlet end 130 and an outlet end 131. The process gas enters the cavity 110 through the inlet end 130, forming a laminar flow in the upper half of the cavity 110. The flow direction of the process gas is as follows: Figure 1 As indicated by the middle arrow. Process gases include, for example, silicon-source precursors or germanium-source precursors. Silicon-source precursors include, for example, silane (SiH4), dichlorosilane (Si2H6), dichlorosilane (SiH2Cl2), tetramethylsilane (C4H12Si), hexachlorodichlorosilane (Si2Cl6), dibromosilane (SiH2Br2), higher silanes, and their derivatives and combinations. Germanium-source precursors include, for example, germanane (GeH4), digermanane (Ge2H6), germanium tetrachloride (GeCl4), dichlorogermanane (GeH2Cl2), and their derivatives and combinations. The silicon-source precursor or germanium-source precursor can be combined with etching gases such as hydrogen chloride (HCl), chlorine (Cl2), and hydrogen bromide (HBr) and introduced into chamber 110.

[0048] like Figure 1 As shown, a bracket 122 is further provided below the base 120. The bracket 122 includes a rotating shaft 123 and multiple support arms 124. The base 120 is connected to the rotating shaft 123 through multiple support arms 124 evenly distributed in the circumferential direction, so that the rotating shaft 123 can support the base 120 and drive the base 120 to rotate around the rotation axis RA.

[0049] A heating assembly 140 is disposed outside the internal volume 111 for heating the wafer 121. The heating assembly 140 includes multiple lamp groups 141 arranged around the internal volume 111. The multiple lamp groups 141 can heat the base 120 and the wafer 121 through radiative heat transfer, so that the process gas entering the cavity 110 through the gas inlet 130 is uniformly diffused and decomposed on the surface of the wafer 121, and by-product gases and excess process gases can be extracted through the gas outlet 131.

[0050] The semiconductor device 100 also includes an upper high-temperature gauge 151 and a lower high-temperature gauge 152 disposed outside the cavity 110. The upper high-temperature gauge 151 is used to monitor the surface temperature of the wafer 121 inside the cavity 110, and the lower high-temperature gauge 152 is used to monitor the temperature of the back side of the base 120. Correspondingly, the plurality of lamp groups 147 arranged around the internal volume 111 can be divided into an upper lamp group 143 disposed above the cavity 110 and a lower lamp group 144 disposed below the cavity 110 to provide more uniform heating of the wafer 121. Based on the temperatures detected by the upper high-temperature gauge 151 and the lower high-temperature gauge 152, the heating power of the heating assembly 140 can be adaptively adjusted.

[0051] like Figure 1 As shown, the semiconductor device 100 also includes a plurality of lifting pins 161 and lifting shafts 162 for moving the wafer 121 up and down. Further reference Figure 2 Corresponding to the multiple lifting pins 161, the base 120 has multiple mounting holes 125 evenly spaced circumferentially for mounting the lifting pins 161. A limiting part 163 is provided at the top of each lifting pin 161 to prevent it from falling out of the mounting hole 125. To achieve the lifting of the wafer 121, the support arm 124 has through holes 126 at corresponding positions for the lower end of the lifting pin 161 to pass through. Thus, when the lifting shaft 162 is raised or lowered, the multiple lifting arms 164 evenly arranged around the lifting shaft 162 can abut against the lower end of the lifting pin 161, further driving the wafer 121 to rise or fall. The through holes 126 also facilitate further limiting of the lifting pins 161, which helps ensure the stability of the lifting process of the lifting pins 161 and the wafer 121.

[0052] like Figure 3 As shown, the lower pyrometer 152 is used to monitor the temperature on the back of the base 120. It is positioned at the lower end of the support 122 and measures the temperature at the center of the back of the base 120 at a fixed angle. During the rotation of the base 120 and wafer 121 by the support 122, multiple support arms 124 inevitably obstruct the detection optical path of the lower pyrometer 152, thus affecting the accuracy of the measurement results. Figure 4 As shown, the horizontal axis represents time, and the vertical axis represents temperature. The temperature at the susceptor (base) is the temperature measured by the pyrometer 152 when there is no obstruction, and the temperature at the shader (support) is the temperature measured by the pyrometer 152 when there is obstruction. Due to the temperature difference between the support arm 124 of the support 122 and the back of the base 120, the temperature measurement curve of the pyrometer 152 will fluctuate significantly when obstruction occurs.

[0053] Based on this issue, such as Figure 6 As shown, this embodiment provides a base temperature detection method, including:

[0054] Step S1: During the rotation of the base 120 driven by the support 122 in the semiconductor device 100, each rotation cycle of the base 120 is sequentially divided into multiple detection intervals. These multiple detection intervals include an abnormal detection interval where the detection optical path of the lower pyrometer 152, used to detect the center temperature of the base 120, is blocked by the support 122, and a normal detection interval where the detection optical path of the lower pyrometer 152 is not blocked by the support 122.

[0055] Step S2: Determine whether the current detection interval is an abnormal detection interval.

[0056] When the current detection range is a normal detection range, since the detection optical path of the lower pyrometer 152 is not interfered with, the temperature detection value of the lower pyrometer 152 in the current detection range can be directly used as the effective temperature value of the current detection range.

[0057] When the current detection interval is an abnormal detection interval, the predicted temperature value of the current detection interval is obtained based on the effective temperature values ​​of the previous N detection intervals, and this predicted temperature value is used as the effective temperature value of the current detection interval. Where N≥2.

[0058] Based on the effective temperature values ​​of each detection range obtained through the above steps, the heating power of the heating component can be accurately adjusted, which helps to ensure product yield.

[0059] like Figure 5 As shown (horizontal axis: time; vertical axis: temperature), the original temperature measurement trace of the lower pyrometer 152 (without processing by the method of this embodiment) is black, and this black original temperature measurement trace shows obvious fluctuations when the bracket 122 blocks the detection optical path. In contrast, a blue temperature trace is obtained after processing with the base temperature detection method of this embodiment. Figure 5 It is clearly shown that the technical solution of this embodiment significantly suppresses the temperature data anomaly caused by the obstruction of the detection optical path. The smoothness of the blue temperature trace is significantly better than that of the original black trace, that is, the temperature fluctuation amplitude of the blue temperature trace is significantly lower than that of the original black trace.

[0060] As those skilled in the art will understand, since the lower pyrometer 152 has a fixed acquisition period, that is, it acquires a temperature value once at fixed time intervals, the lower pyrometer 152 can acquire multiple raw temperature values ​​at fixed time intervals within each detection interval. Furthermore, the average value of the multiple raw temperature values ​​can be calculated, and the calculated average value can be used as the temperature detection value for the corresponding detection interval.

[0061] In some embodiments, each rotation cycle of the base 120 can be divided into multiple detection intervals of equal duration to ensure that the lower pyrometer 152 can collect the same number of raw temperature values ​​in each detection interval. Furthermore, the number of detection intervals in each rotation cycle can be determined based on the rotational speed of the base 120, thereby determining the duration of each detection interval so that the lower pyrometer 152 can collect a sufficient number of raw temperature values ​​in a single detection interval.

[0062] For example, such as Figure 7 As shown, when the bracket 122 drives the base 120 to rotate at a speed of 32 rpm, each rotation cycle can be divided into 19 detection intervals, and the duration of each detection interval is approximately 0.1 s. Based on the length of each detection interval, the lower pyrometer 152 can perform 5 temperature acquisitions in a single detection interval, and use the average of the 5 acquired raw temperature values ​​as the temperature detection value of the current detection interval.

[0063] Because there is a certain temperature difference between the support arm 124 of the bracket 122 and the back of the base 120, this embodiment also provides a method for determining whether the current detection interval is an abnormal detection interval, including: in step S2, when the difference between the temperature detection value of the current detection interval and the effective temperature value of the previous detection interval is less than or equal to a preset threshold, the current detection interval is determined to be a normal detection interval; when the difference between the temperature detection value of the current detection interval and the effective temperature value of the previous detection interval is greater than the preset threshold, the current detection interval is determined to be an abnormal detection interval. Preferably, the preset threshold can be 5℃, that is, if the difference between the temperature detection value of the current detection interval and the effective temperature value of the previous detection interval is greater than 5℃, the current detection interval is determined to be an abnormal detection interval; otherwise, the current detection interval is determined to be a normal detection interval.

[0064] Furthermore, when the current detection interval is judged to be an abnormal detection interval, the temperature prediction value of the current detection interval can be predicted based on the effective temperature values ​​of the previous N detection intervals, and the temperature prediction value can be used as the effective temperature value of the current detection interval.

[0065] Specifically, refer to Figure 7 In step S1, when each rotation cycle of the base is divided into multiple detection intervals, each detection interval is numbered sequentially. By constructing a linear regression model using the effective temperature values ​​and numbers of the N previous detection intervals, and inputting the number of the current detection interval into the linear regression model, the predicted temperature value of the current detection interval can be obtained.

[0066] For example, the equation corresponding to the desired linear regression model is y = bx + a, where x represents the detection interval number and y represents the effective temperature value of the detection interval. The values ​​of constants a and b can be determined using the following formula:

[0067]

[0068] in, The average value of the numbers of the N detection intervals; x is the average of the effective temperature values ​​across N detection intervals; i Let y be the number of the i-th detection interval out of N detection intervals; i Let be the effective temperature value of the i-th detection interval out of N detection intervals.

[0069] In some embodiments, the effective temperature values ​​of the previous N detection intervals can be filtered to obtain the effective temperature value of the current detection interval.

[0070] In some embodiments, when the current detection interval is an abnormal detection interval and the previous detection interval is a normal detection interval, the N detection intervals include at least two normal detection intervals between the current detection interval and the previous abnormal detection interval.

[0071] In other embodiments, when the current detection interval is an abnormal detection interval, and the previous detection interval is also an abnormal detection interval, the N detection intervals include: the previous detection interval; and all detection intervals used to predict the effective temperature value of the previous detection interval. For example, refer to... Figure 7 When two consecutive abnormal detection intervals occur, the effective temperature value of the second abnormal detection interval can be predicted by combining the effective temperature value obtained after prediction of the first abnormal detection interval and the effective temperature values ​​of multiple normal detection intervals used to predict the effective temperature value of the first abnormal detection interval.

[0072] Understandably, when making predictions by constructing a linear regression model, since the effective temperature value of the first anomaly detection interval is calculated using the linear regression model, the effective temperature value of the second anomaly detection interval can be directly calculated using the same linear regression model used for the first anomaly detection interval.

[0073] In some embodiments, when the current detection range is an abnormal detection range obscured by a support arm 124, the N detection ranges include all normal detection ranges between the current detection range and the abnormal detection range obscured by the previous support arm 124 during the rotation of the base 120. For example, refer to Figure 7The abnormal detection interval T6, where the detection optical path of the pyrometer 152 is blocked by the support arm 124, is taken as the current detection interval, and the abnormal detection interval blocked by the previous support arm 124 is taken as the interval T0. A linear regression model can be constructed by using the effective temperature values ​​and numbers of the five detection intervals between T6 and T0, namely intervals T1 to T5. The number of the current interval T6 is input into the linear regression model as the effective temperature value of interval T6.

[0074] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0075] It should be noted that the apparatus and methods disclosed in the embodiments herein can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings show the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments herein. In this regard, each block in a flowchart or block diagram may represent a module, program, or part of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system to perform the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0076] In addition, the functional modules in the various embodiments of this article can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0077] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for detecting the base temperature of a semiconductor device, characterized in that, The base temperature detection method includes: Step S1: Divide each rotation cycle of the base into multiple detection intervals in sequence; the multiple detection intervals include an abnormal detection interval where the detection optical path of the pyrometer used to detect the temperature on the back of the base is blocked by the bracket and a normal detection interval where the detection optical path of the pyrometer is not blocked by the bracket. Step S2: When the current detection interval is an abnormal detection interval, the temperature prediction value of the current detection interval is predicted based on the effective temperature values ​​of the previous N detection intervals, and the predicted temperature value is used as the effective temperature value of the current detection interval; where N≥2.

2. The base temperature detection method according to claim 1, characterized in that, In step S2, when the current detection interval is a normal detection interval, the temperature detection value of the pyrometer in the current detection interval is taken as the effective temperature value of the current detection interval.

3. The base temperature detection method according to claim 2, characterized in that, In step S2, when the difference between the temperature detection value of the current detection interval and the effective temperature value of the previous detection interval is less than or equal to a preset threshold, the current detection interval is determined to be a normal detection interval. If the difference between the temperature value detected in the current detection interval and the effective temperature value in the previous detection interval is greater than a preset threshold, the current detection interval is determined to be an abnormal detection interval.

4. The base temperature detection method according to claim 1, characterized in that, The semiconductor device further includes a heating component, and the base temperature detection method further includes: adjusting the heating power of the heating component based on the obtained effective temperature value.

5. The base temperature detection method according to claim 1, characterized in that, Step S1 includes: when dividing each rotation cycle of the base into multiple detection intervals, numbering each detection interval sequentially. In step S2, the step of predicting the temperature prediction value of the current detection interval based on the effective temperature values ​​of the previous N detection intervals includes: constructing a linear regression model based on the effective temperature values ​​and numbers of the N detection intervals, and inputting the number of the current detection interval into the linear regression model to obtain the temperature prediction value of the current detection interval.

6. The base temperature detection method according to claim 1, characterized in that, In step S2, when the current detection interval is an abnormal detection interval and the previous detection interval is a normal detection interval, the N detection intervals include at least two normal detection intervals between the current detection interval and the previous abnormal detection interval.

7. The base temperature detection method according to claim 1, characterized in that, In step S2, when the current detection interval is an abnormal detection interval and the previous detection interval is an abnormal detection interval, the N detection intervals include: the previous detection interval; and all detection intervals used to predict the effective temperature value of the previous detection interval.

8. The base temperature detection method according to claim 1, characterized in that, The bracket includes a rotating shaft and multiple support arms. The base is connected to the rotating shaft through the multiple support arms that are evenly distributed circumferentially. The rotating shaft drives the base to rotate through the multiple support arms. During one rotation cycle of the base, the plurality of support arms sequentially block the detection optical path of the pyrometer to form a plurality of abnormal detection intervals.

9. The base temperature detection method according to claim 8, characterized in that, In step S2, when the current detection interval is an abnormal detection interval blocked by a support arm, the N detection intervals include: all normal detection intervals between the current detection interval and the abnormal detection interval blocked by the previous support arm during the rotation of the base.

10. The base temperature detection method according to claim 1, characterized in that, In each detection interval, the pyrometer collects multiple raw temperature values ​​at fixed time intervals, and the average value of the multiple raw temperature values ​​is used as the temperature detection value.

11. The base temperature detection method according to claim 1, characterized in that, Step S1 includes: dividing each rotation cycle of the base into multiple detection intervals of equal duration.

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