High-reliability super junction structure with adjustable super junction column spacing

Abstract

The invention discloses a high-reliability super junction structure with adjustable super junction column spacing. The high-reliability super junction structure comprises an epitaxial layer, a first super junction column combined structure and two second super junction column combined structures. The first super junction column composite structure comprises M second doping type first super junction columns which are symmetrical along the central axis, the M first super junction columns are arranged in the epitaxial layer in parallel, and the width of each first super junction column is gradually reduced from the center to the end part in the first direction; the two second super junction column combined structures are symmetrically arranged on the two sides of the first super junction column combined structure in the second direction, each second super junction column combined structure comprises N second super junction columns of a second doping type which are symmetrical along the central axis, and the N second super junction columns are arranged in the epitaxial layer in parallel. According to the invention, the electric field concentration phenomenon at the edge of the terminal is effectively relieved, and the electric field distribution of the terminal is improved, so that the voltage resistance and reliability of the super-junction structure are improved, and the terminal efficiency and the blocking capability are improved.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor technology, and specifically relates to a high-reliability superjunction structure with adjustable superjunction pillar spacing. Background Technology

[0002] Superjunction (SJ) technology is a high-voltage power device structure based on the charge balance principle. By alternately forming P-type and N-type doped regions (P-pillars and N-pillars) in the drift region, the on-resistance can be significantly reduced while maintaining a high breakdown voltage, thus balancing the device's conduction performance and breakdown voltage performance. This technology has been widely used in silicon-based and silicon carbide (SiC) power MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors).

[0003] Traditional terminations often employ a circular arc-shaped layout. However, for superjunction structures, the different P / N ratios at the termination corners and edges can easily disrupt charge balance, leading to problems such as electric field concentration and premature breakdown at the corners. To avoid this issue, existing technologies typically use equidistant parallel strip termination structures to maintain a consistent P / N ratio throughout the termination, thereby ensuring device performance.

[0004] However, this structure limits the terminal efficiency and is prone to electric field concentration at the terminal edge, affecting the device's blocking capability and reliability. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a highly reliable superjunction structure with adjustable superjunction column spacing.

[0006] The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a high-reliability superjunction structure with adjustable superjunction column spacing, comprising: Epitaxial layer of the first doping type; The first superjunction pillar assembly structure includes M first superjunction pillars of the second doped type that are symmetrical along the central axis. The M first superjunction pillars are arranged parallel to each other in the epitaxial layer. Each first superjunction pillar extends from a first position in the epitaxial layer to a second position in the epitaxial layer along the thickness direction. The width of each first superjunction pillar gradually decreases from the center to the end along a first direction, where the first direction is the direction from the center to the end of the first superjunction pillar. Two second superjunction pillar combination structures are symmetrically arranged on both sides of the first superjunction pillar combination structure along a second direction. Each second superjunction pillar combination structure includes N second superjunction pillars of the second doping type symmetrically arranged along the central axis. The N second superjunction pillars are arranged parallel to each other in the epitaxial layer. Each second superjunction pillar extends from a first position in the epitaxial layer to a second position in the epitaxial layer along the thickness direction. The second direction is the direction from the center of the epitaxial layer to the edge. The first direction and the second direction are perpendicular to each other and both are perpendicular to the thickness direction. M and N are integers greater than 0. The first doping type and the second doping type are opposite in type.

[0007] In one embodiment of the present invention, the first superstructure includes two symmetrically arranged partial superstructures, each of the partial superstructures including P sequentially connected sub-superstructures, and the width of the P sub-superstructures gradually decreases along the first direction. In one embodiment of the present invention, the number P of sub-superstructures of each of the partial superstructures is equal to the number N of the second superstructures in each second superstructure combination structure.

[0008] In one embodiment of the present invention, all the second superstructure columns have the same width; Along the second direction, the distance between two adjacent second superstructure columns gradually increases.

[0009] In one embodiment of the present invention, along the second direction, the width of the N second superstructures in the second superstructure combination structure gradually decreases, and the distance between any two adjacent second superstructures is equal. In one embodiment of the present invention, the ratio of the width of the nth sub-superstructure of one of the mth first superstructures to a first distance is equal to the ratio of the width of the nth second superstructure to a second distance, wherein the first distance is the distance between two adjacent nth sub-superstructures, the second distance is the distance between the (n-1)th and nth second superstructures, and 1≤m≤M, 1≤n≤N.

[0010] In one embodiment of the present invention, the high-reliability superjunction structure further includes: The active region of the second doping type extends from the upper surface of the epitaxial layer to the second position of the epitaxial layer; A transition region of the second doping type is disposed around the active region and extends from the upper surface of the epitaxial layer to a second position of the epitaxial layer; A second doped surface termination structure is disposed around the transition region and extends from the upper surface of the epitaxial layer to a second position of the epitaxial layer. In one embodiment of the present invention, the sub-superstructure pillar with the largest width is projected along the thickness direction onto the upper surface of the active region, and is at least partially located in the region where the active region is located. In one embodiment of the present invention, the distance between the first side of the surface terminal structure and the first side of the first superstructure along the first direction is equal to the distance between the second side of the surface terminal structure and the outer side of the second superstructure farthest from the center of the epitaxial layer along the second direction, wherein the first side and the second side are perpendicular to each other. In one embodiment of the present invention, the doping concentrations of the epitaxial layer, the first superjunction pillar, and the second superjunction pillar are equal.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: The superjunction structure design provided by this invention has a first superjunction pillar with a gradually decreasing width, that is, the width of each first superjunction pillar gradually decreases from the center to the end along the first direction. This allows the terminal to smoothly transition from an n-rich region (with a higher concentration of n-type doping) to a p-rich region (with a higher concentration of p-type doping) or from a p-rich region to an n-rich region. This effectively alleviates the electric field concentration phenomenon at the edge of the terminal and improves the electric field distribution at the terminal. As a result, the voltage withstand capability and reliability of the superjunction structure are improved, as well as the terminal efficiency and blocking capability. At the same time, it takes into account the feasibility of the process and the flexibility of the design.

[0012] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0013] Figure 1 This is a partial layout diagram of a high-reliability superjunction structure with adjustable superjunction column spacing provided in an embodiment of the present invention; Figure 2 The embodiments of the present invention provide, as shown below. Figure 1 A schematic cross-sectional view of part of the layout structure along AA' is shown; Figure 3 The embodiments of the present invention provide, as shown below. Figure 1 A schematic cross-sectional view of part of the layout structure along BB'; Figure 4 This is a schematic diagram of the first superstructure column combination structure provided in an embodiment of the present invention; Figure 5 This is a partial layout diagram of another high-reliability superjunction structure with adjustable superjunction column spacing provided in an embodiment of the present invention; Figure 6This is another embodiment of the present invention. Figure 1 The diagram shows a cross-sectional view of part of the layout structure along AA'. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0015] Example 1 Please see Figure 1 , Figure 2 and Figure 3 , Figure 1 This is a partial layout diagram of a high-reliability superjunction structure with adjustable superjunction column spacing provided in an embodiment of the present invention. Figure 2 The embodiments of the present invention provide, as shown below. Figure 1 The diagram shows a partial cross-sectional view of the layout structure along AA'. Figure 3 The embodiments of the present invention provide, as shown below. Figure 1 The diagram shown is a cross-sectional view along BB' of a partial layout structure. This embodiment of the invention provides a high-reliability superjunction structure with adjustable superjunction column spacing. This high-reliability superjunction structure is a mechanism symmetrical along a central axis, and includes: Epitaxial layer 1 of the first doping type; The first superjunction pillar assembly structure includes M first superjunction pillars 2 of the second doped type, symmetrically arranged along a central axis. The M first superjunction pillars 2 are arranged parallel to each other within the epitaxial layer 1. Along the thickness direction, each first superjunction pillar 2 extends from a first position within the epitaxial layer 1 to a second position within the epitaxial layer 1. Along a first direction, the width of each first superjunction pillar 2 gradually decreases from its center to its end. The first direction is the direction from the center to the end of the first superjunction pillar 2, and the width direction is... Figure 1 The vertical direction in; Two second superjunction pillar combination structures are symmetrically arranged on both sides of the first superjunction pillar combination structure along the second direction. Each second superjunction pillar combination structure includes N second superjunction pillars 3 of the second doped type symmetrically arranged along the central axis. The N second superjunction pillars 3 are arranged parallel to each other in the epitaxial layer 1. Each second superjunction pillar 3 extends from a first position in the epitaxial layer 1 to a second position in the epitaxial layer 1 along the thickness direction. The second direction is the direction from the center to the edge of the epitaxial layer. The first direction and the second direction are perpendicular to each other and both are perpendicular to the thickness direction. M and N are integers greater than 0. The first doping type and the second doping type are opposite in that the first doping type is p-type doping and the second doping type is n-type doping, and vice versa.

[0016] Specifically, in this embodiment, a first superpillar assembly structure is provided within the epitaxial layer 1. This first superpillar assembly structure includes M parallel first superpillars 2, all of which have the same depth within the epitaxial layer 1. They extend from a first position within the epitaxial layer 1 to a second position within the epitaxial layer 1, with the first position located above the second position. Both ends of the first superpillars 2 are also within the epitaxial layer 1. All first superpillars 2 have the same length, and their length direction is [missing information]. Figure 1 Horizontal direction in the middle, along Figure 1 In the first direction, from the center of the first superjunction pillar 2 to its end, the width of the first superjunction pillar 2 gradually decreases, and the distance between two adjacent first superjunction pillars 2 is equal. This allows the first superjunction pillars 2 to become narrower and narrower, which is equivalent to the spacing of the first superjunction pillars 2 gradually widening at the edge of the transition region, so as to better homogenize the electric field.

[0017] Furthermore, two second superstructures are provided within the epitaxial layer 1. The two second superstructures are symmetrically arranged on both sides of the first superstructure along the second direction. Each second superstructure includes N parallel second superstructures 3. The first to the Nth second superstructures 3 are arranged sequentially from the direction away from the first superstructure. The first superstructure 2 and the second superstructure 3 are also parallel to each other. All the second superstructures 3 have the same depth within the epitaxial layer 1. The first superstructure 2 and the second superstructure 3 also have the same depth. They extend from a first position within the epitaxial layer 1 to a second position within the epitaxial layer. Both ends of the second superstructure 3 are also within the epitaxial layer 1. All the second superstructures 3 have the same length. The first superstructure 2 and the second superstructure 3 also have the same length.

[0018] In one specific embodiment, the high-reliability superjunction structure further includes: The active region 4 of the second doping type extends from the upper surface of the epitaxial layer 1 to the second position of the epitaxial layer 1; The transition region 5 of the second doping type is disposed around the active region 4 and extends from the upper surface of the epitaxial layer 1 to the second position of the epitaxial layer 1. The second doped type surface termination structure 6 is disposed around the transition region 5 and extends from the upper surface of the epitaxial layer 1 to the second position of the epitaxial layer 1.

[0019] In an optional embodiment, the first superjunction pillar 2 includes two symmetrically arranged partial superjunction pillars, each of which includes P sequentially connected sub-superjunction pillars 21. Along a first direction, the width of the P sub-superjunction pillars 21 gradually decreases. By gradually decreasing the width of the P sub-superjunction pillars 21, the spacing between adjacent sub-superjunction pillars 21 at the edge of the transition region gradually widens, resulting in a better uniform electric field. For example, if P is 4, ... Figure 4As shown, WP21 > WP22 > WP23 > WP24 are equal, and the distance between two adjacent sub-superstructure pillars 21 gradually increases along the first direction, i.e., W21 < W22 < W23 < W24.

[0020] In an optional embodiment, the number P of sub-superjunction pillars 21 of each partial superjunction pillar is equal to the number N of second superjunction pillars in each second superjunction pillar combination structure, such that the charge balance of the terminals in the first and second directions is consistent, i.e., N=P.

[0021] Preferably, the values ​​of N and P are in the range of 3 to 8.

[0022] Preferably, the value of M is in the range of 20 to 50.

[0023] In one specific embodiment, the second superstructure 3 in the second superstructure composite structure has two structural forms.

[0024] The first structural form: such as Figure 1 As shown, all second superjunction pillars 3 have equal widths. Along the second direction, the distance between adjacent second superjunction pillars 3 gradually increases. By using second superjunction pillars 3 of equal width and setting the distance between adjacent second superjunction pillars 3 to gradually increase, the spacing of the second superjunction pillars 3 at the edge of the transition region is gradually widened, which can better unify the electric field. The distance between the first second superjunction pillar 3 and the first superjunction pillar 2 closest to it is less than the distance between the first and second second superjunction pillars 3. The distance between the nth and (n+1th)th second superjunction pillars 3 is less than the distance between the (n+1th)th and (n+2th)th second superjunction pillars 3. For example... Figure 1 As shown, N is 4, therefore, W31 < W32 < W33 < W34.

[0025] The second structural form: such as Figure 5 As shown, along the second direction, the width of the N second superjunction pillars 3 in the second superjunction pillar combination structure gradually decreases, and the distance between any two adjacent second superjunction pillars 3 is equal. By maintaining the equal distance between adjacent second superjunction pillars 3 and gradually decreasing the width of the N second superjunction pillars 3, the spacing of the second superjunction pillars 3 at the edge of the transition region gradually widens, which can better homogenize the electric field, for example, as... Figure 5 As shown, N is 4, and W31=W32=W33=W34.

[0026] Furthermore, the ratio of the width of the nth sub-superjunction pillar 21 of one part of the mth first superjunction pillar 2 to the first distance is equal to the ratio of the width of the nth second superjunction pillar 3 to the second distance, so that the charge balance of the terminal is consistent in the first and second directions. The first distance is the distance between two adjacent nth sub-superjunction pillars 21, and the 1st to Nth sub-superjunction pillars 21 are arranged sequentially along the first direction. The second distance is the distance between the (n-1)th and nth second superjunction pillars 3, 1≤m≤M, 1≤n≤N.

[0027] For example Figure 1 In the first structural form shown, all the second superstructure columns 3 have the same width, denoted as WP3. Therefore, WP21 / W21 = WP3 / WP31, WP22 / W22 = WP2 / WP32, WP23 / W23 = WP3 / WP33, and WP24 / W24 = WP3 / WP34. For example... Figure 5 In the first structural form shown, the relationship between the widths of the four second super-structures in the second super-structure is WL31 < WL32 < WL33 < WL34. Therefore, WP21 / W21 = WL31 / W31, WP22 / W22 = WL32 / W32, WP23 / W23 = WL33W33, and WP24 / W24 = WL34 / W34.

[0028] In an optional embodiment, the widest sub-superstructure pillar 21 is projected along the thickness direction onto the upper surface of the active region 4, and is at least partially located in the region where the active region 4 is located.

[0029] In an optional embodiment, such as Figure 1 , Figure 5 As shown, along the first direction, the distance L1 between the first side surface of the surface terminal structure 6 and the first side surface of the first superstructure 2 is equal to the distance L2 between the second side surface of the surface terminal structure 6 and the outer side surface of the second superstructure 3 furthest from the center of the epitaxial layer 1, along the second direction. The first side surface and the second side surface are perpendicular to each other, and the first side surface of the surface terminal structure 6 and the first side surface of the first superstructure 2 are located on the same side, both perpendicular to the first direction. For example, both are... Figure 1 On the left side of the surface terminal structure 6, the second side is perpendicular to the second direction, for example, both are... Figure 1 The upper side of the middle.

[0030] In an optional embodiment, the doping concentrations of the epitaxial layer 1, the first superjunction pillar 2, and the second superjunction pillar 3 are equal.

[0031] Optionally, the doping concentration of epitaxial layer 1, first superjunction pillar 2, and second superjunction pillar 3 ranges from 1e. 16 cm-3 ~2e 17 cm -3 .

[0032] In a specific embodiment, such as Figure 6 As shown, the high-reliability superjunction structure also includes: Gate dielectric layer 7 is disposed on active region 4; Gate 8 is disposed on gate dielectric layer 7; Gate isolation dielectric 9 covers gate 8; The cell source is 10, covered by gate isolation dielectric 9; Terminal dielectric layer 11 is disposed on part of surface terminal structure 6 and exposed epitaxial layer 1; Terminal metal 12 is disposed on part of the transition region 5, the remaining surface terminal structure 6, and part of the terminal dielectric layer 11. Terminal isolation medium 13 is disposed on the remaining transition region 5, and terminal isolation medium 13 is between cell source 10 and terminal metal 12; Substrate layer 14 is disposed on the lower surface of epitaxial layer 1; The drain electrode is disposed on the lower surface of the substrate layer 14.

[0033] Optionally, the epitaxial layer 1 and the substrate layer 14 are made of the same material, which is any semiconductor material used to prepare power semiconductor devices, including silicon, silicon carbide, gallium nitride, gallium oxide, etc.

[0034] The superjunction structure design provided by this invention has a first superjunction pillar with a gradually decreasing width, that is, the width of each first superjunction pillar gradually decreases from the center to the end along the first direction. This allows the terminal to smoothly transition from the n-rich region to the p-rich region or from the p-rich region to the n-rich region, effectively alleviating the electric field concentration phenomenon at the edge of the terminal and improving the electric field distribution at the terminal. This improves the withstand voltage and reliability of the superjunction structure, enhances the terminal efficiency and blocking capability, while taking into account the feasibility of the process and the flexibility of the design.

[0035] The gradient-type terminal superjunction structure provided by this invention makes the electric field distribution more uniform and improves the terminal efficiency. This invention can shorten the terminal length and reduce the ineffective terminal area while ensuring the same withstand voltage, thereby improving the terminal efficiency and chip area utilization.

[0036] The gradient-terminated superjunction structure provided by this invention can better homogenize the electric field. Charge affects the distribution of the electric field, and a more uniform electric field distribution can resist the changes in electric field distribution caused by charge. It has lower sensitivity to charge deviation or interface charge. Even if there are slight doping or geometric errors in the manufacturing process, it can maintain a stable electric field distribution, reduce charge sensitivity, and enhance process tolerance.

[0037] The gradient terminal superjunction structure provided by this invention enhances the designability of the chip and breaks through the limitation that traditional parallel strip structures cannot achieve gradient column spacing.

[0038] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0039] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0040] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0041] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0042] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0043] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A high-reliability superjunction structure with adjustable superjunction column spacing, characterized in that, include: Epitaxial layer of the first doping type; The first superjunction pillar assembly structure includes M first superjunction pillars of the second doped type that are symmetrical along the central axis. The M first superjunction pillars are arranged parallel to each other in the epitaxial layer. Each first superjunction pillar extends from a first position in the epitaxial layer to a second position in the epitaxial layer along the thickness direction. The width of each first superjunction pillar gradually decreases from the center to the end along a first direction, where the first direction is the direction from the center to the end of the first superjunction pillar. Two second superjunction pillar combination structures are symmetrically arranged on both sides of the first superjunction pillar combination structure along a second direction. Each second superjunction pillar combination structure includes N second superjunction pillars of the second doping type symmetrically arranged along the central axis. The N second superjunction pillars are arranged parallel to each other in the epitaxial layer. Each second superjunction pillar extends from a first position in the epitaxial layer to a second position in the epitaxial layer along the thickness direction. The second direction is the direction from the center of the epitaxial layer to the edge. The first direction and the second direction are perpendicular to each other and both are perpendicular to the thickness direction. M and N are integers greater than 0. The first doping type and the second doping type are opposite in type.

2. The high-reliability superjunction structure according to claim 1, characterized in that, The first superstructure includes two symmetrically arranged partial superstructures, each of which includes P sequentially connected sub-superstructures. Along the first direction, the width of the P sub-superstructures gradually decreases.

3. The high-reliability superjunction structure according to claim 2, characterized in that, The number P of sub-superstructures in each of the aforementioned partial superstructures is equal to the number N of second superstructures in each second superstructure combination structure.

4. The high-reliability superjunction structure according to claim 2, characterized in that, All the second superstructure columns have the same width; Along the second direction, the distance between two adjacent second superstructure columns gradually increases.

5. The high-reliability superjunction structure according to claim 2, characterized in that, Along the second direction, the width of the N second superstructures in the second superstructure combination structure gradually decreases, and the distance between any two adjacent second superstructures is equal.

6. The high-reliability superjunction structure according to claim 4 or 5, characterized in that, The ratio of the width of the nth sub-superstructure of one of the mth first superstructures to the first distance is equal to the ratio of the width of the nth second superstructure to the second distance, wherein the first distance is the distance between two adjacent nth sub-superstructures, the second distance is the distance between the (n-1)th and nth second superstructures, and 1≤m≤M, 1≤n≤N.

7. The high-reliability superjunction structure according to claim 2, characterized in that, Also includes: The active region of the second doping type extends from the upper surface of the epitaxial layer to the second position of the epitaxial layer; A transition region of the second doping type is disposed around the active region and extends from the upper surface of the epitaxial layer to a second position of the epitaxial layer; A second doped surface termination structure is disposed around the transition region and extends from the upper surface of the epitaxial layer to a second position of the epitaxial layer.

8. The high-reliability superjunction structure according to claim 7, characterized in that, The sub-superstructure pillar with the largest width is projected along the thickness direction onto the upper surface of the active region, and is at least partially located in the region where the active region is located.

9. The high-reliability superjunction structure according to claim 7, characterized in that, Along the first direction, the distance between the first side of the surface terminal structure and the first side of the first superstructure pillar is equal to the distance between the second side of the surface terminal structure and the outer side of the second superstructure pillar furthest from the center of the epitaxial layer, along the second direction, wherein the first side and the second side are perpendicular to each other.

10. The high-reliability superjunction structure according to claim 1, characterized in that, The epitaxial layer, the first superjunction pillar, and the second superjunction pillar have the same doping concentration.

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