Substrate for a power electronic circuit

Abstract

A substrate (1) divided into several regions, having a plurality of central regions (100), each having a planar metal lamination and intended to form individual sub-substrates by dividing the substrate (1), for a power electronic circuit, having a planar insulating body (2) and having planar metallic conductor tracks arranged on its second main surface and having planar metal laminations (3) arranged on its first main surface (20), and having sub-laminations arranged circumferentially around the metal lamination of the sub-substrates present after singulation and also circumferentially on an edge region, wherein a first sub-lamination (4) and a second sub-lamination (5) thereof are arranged on or adjacent to an outer edge (22) of the insulating body (2), and wherein the two sub-laminations (4,5) are at least partially separated from one another by a trench (6) preferably extending to the first main surface (20), and wherein the trench (6) either has a dam (7), wherein the trench (6) is partially filled with a dam material (70), thus maintaining a residual trench (66), wherein the design of the dam material (70) satisfies the following conditions: , • viewed in the direction of the trench (600), the maximum cross-sectional area (800) of the dam material is at least 30% and a maximum of 70% of the clear cross-sectional area (820) of the trench (6); • viewed in the trench direction (600), the length (802) of the dam material (70) is at least 50% of the clear depth (824) of the trench (6); or has a trench structure (9) in which the trench (6) has no clear passage area (810) or a maximum of 50% of the clear cross-sectional area (820) or has a mixed form of dam (7) and trench structure (9).

Description

[0001] The invention describes a power electronic circuit with a planar insulating body and with planar metallic conductor tracks arranged on its second main surface and with planar metal laminations arranged on its first main surface. Generic substrates are known in particular as so-called DCB - direct copper bonding - substrates and their derivatives. When these substrates are present as multiple panels, it is known that a first partial lamination and a second partial lamination of the metal lamination are arranged on or adjacent to an outer edge of the insulating body, wherein both partial laminations are separated from one another by a trench extending to the first main surface. Furthermore, the invention describes a manufacturing method for a specific embodiment of said substrate.

[0002] DE 43 19 944 A1 discloses such a generic multiple substrate with a ceramic layer which forms at least two adjoining and integrally connected grooves, each of which is provided with at least one metallization or metal surface on at least one surface side of the ceramic layer, as well as a method for its production.

[0003] US 2009 / 0 174 063 A1 discloses a semiconductor module comprising a ceramic substrate having a front surface on which a semiconductor element is mounted and a rear surface on the opposite side of the front surface, a front metal plate connected to the front surface, a rear metal plate connected to the front surface to the rear surface, and a heat sink connected to the rear metal plate. The rear metal plate includes a connection surface facing the heat sink. The connection surface includes a connection region and a non-connection region. The non-connection region includes recesses extending in the thickness direction of the rear metal plate. The connection area of ​​the rear metal plate is in a range of 65% to 85% of the total area of ​​the connection surface on the rear metal plate.

[0004] DE 10 2013 013 842 A1 discloses a method for producing metal-ceramic substrates with a ceramic layer and with at least one metallization and / or with at least one structured metallization forming metal regions on at least one surface side of the ceramic layer, wherein after the application of the at least one metallization and / or the metal regions, cracks that are present at the edge region of the at least one metallization or the metal regions between the ceramic of the ceramic layer and the metal of the at least one metallization or the metal regions and / or that extend into the ceramic of the ceramic layer are filled or pressed with a curable or polymerizable sealing and / or pressing compound, wherein the filling or pressing of the cracks takes place in such a way thatthat after filling or pressing, the sealing and / or grouting compound is absorbed exclusively or substantially exclusively in the cracks and after filling or pressing, edge regions of the at least one metallization are not covered by the sealing and / or grouting compound at least over the greater part of the height or thickness dc of the metallization.

[0005] Furthermore, EP 0 330 895 A2 discloses a device for attaching electronic components, in particular power semiconductors, to substrates by means of a pressure sintering process, in which the surfaces to be joined are subjected to a pressure of at least 900 N / cm 2pressed together. Components with a structured upper surface can be pressure sintered if they are placed together with a body made of elastically deformable material, e.g., silicone rubber, into a receiving chamber sealed by a movable die that transmits the sintering pressure. The deformable body completely fills the remaining interior of the receiving chamber when the sintering pressure is reached.

[0006] When using the aforementioned multiple substrate within the framework of the aforementioned method for the material-to-material attachment of, for example, power semiconductor components to the conductor tracks of such a substrate, the following disadvantageous situation arises in particular: The insulating material body of the substrate has a flat metal lamination on its first main surface facing away from the conductor tracks, wherein a first partial lamination and a second partial lamination are arranged adjacent to an outer edge of the insulating material body and wherein the two partial laminations are separated from one another by a trench. During the method, the deformable body, the so-called sintering pad, undergoes a transition to a state similar to liquefaction with a high viscosity due to the applied pressure. The sintering pad thus becomes viscoelastic and can penetrate into the trench.After the pressurization process is terminated, part of the sintering pad remains in this trench, causing damage to the pad. This mechanism limits the service life, i.e., the number of possible uses, of the sintering pad.

[0007] In view of the state of the art and the disadvantageous situation described, the invention is based on the object of further developing a substrate for power electronic circuits in such a way that the sintering pad is largely protected from damage when a connection partner is sintered to this substrate.

[0008] This object is achieved according to the invention by a substrate divided into several regions with a plurality of central regions, each of which has a planar metal lamination and which are intended to form individual sub-substrates by dividing the substrate, for a power electronic circuit with a planar insulating material body and with planar metallic conductor tracks arranged on its second main surface and with planar metal laminations arranged on its first main surface, wherein partial laminations are arranged circumferentially around the sub-substrates present after the separation and also circumferentially on an edge region,wherein a first partial lamination and a second partial lamination thereof are arranged on or adjacent to an outer edge of the insulating material body, and wherein both partial laminations are at least partially separated from one another by a trench preferably extending to the first main surface, and wherein the trench either has a dam, wherein the trench is partially filled with a dam material, thus maintaining a residual trench, wherein the configuration satisfies the following conditions: (a) viewed in the direction of the trench, the maximum cross-sectional area of ​​the embankment material shall be at least 30% and at most 70% of the clear cross-sectional area of ​​the trench; b) viewed in the direction of the trench, the length of the embankment material is at least 50% of the clear depth of the trench; or has a trench structure in which the trench has no clear passage area or a maximum clear cross-sectional area of ​​50% of the clear cross-sectional area or has a mixed form of embankment and trench structure

[0009] The term "trench" is understood here and below to refer to an imaginary gap between two partial metallizations, extending from adjacent sections of the respective surface of the partial metallization facing away from the insulating body toward the insulating body and spatially separating the two partial metallizations from each other. A "dam" is then the partial filling of such a trench with a dam material, viewed in the longitudinal direction or trench direction. Filling the trench with a dam material leaves a real remainder of the trench, i.e., a permanent residual trench.The term "clear cross-sectional area" refers to the area of ​​the trench, or more precisely the remaining trench, viewed in the trench direction, which is formed by the first main surface of the insulating material body, the two side walls of the trench, and the imaginary connecting line between the two surfaces of the partial claddings adjacent to the side walls. The "clear depth" of the trench, or more precisely the remaining trench, refers to the vertical distance between the surface of the two equally thick partial claddings and the first main surface of the insulating material body. The "clear passage area" refers to the cross-sectional area, viewed in the trench direction, which results from the projection onto the trench entrance, i.e. the opening of the trench at the outer edge of the insulating material.

[0010] On the one hand, it can be advantageous if the dam material is designed as a first dam material that is identical to the material of the partial laminations, and advantageously the two partial laminations and the first dam material are designed as a single piece. This design then therefore has a partially imreal trench. The two partial laminations were therefore never two-piece during production. Rather, the existing space between the partial laminations was formed in particular by means of the method described below. On the other hand, it can be advantageous if the dam material is designed as a second dam material that is different from the material of the two partial laminations and is either metallic or non-metallic, preferably as a plastic, preferably as an epoxy resin.

[0011] It may also be preferred if, viewed in the direction of the trench, the length of the dam material is a maximum of 50%, preferably a maximum of 30%, of the length 822 of the trench.

[0012] In principle, it may be preferable for the outer edge of the dam material to be directly aligned with the adjacent outer edge of the first and second partial cladding. Alternatively, it may be preferable for the outer edge of the dam material to be set back into the trench relative to the adjacent outer edge of the two partial claddings by a maximum of 10 times the clear depth of the trench.

[0013] In principle, it is advantageous if the respective outer edge of the two partial claddings adjacent to the trench is aligned with the corresponding outer edge of the insulating body. Alternatively, it may be advantageous if the respective outer edge of the two partial claddings adjacent to the trench is set back from the corresponding outer edge of the insulating body by a maximum of 10 times, in particular by 5 times, the thickness of the two partial claddings, which is the same for both.

[0014] In particular, it may be advantageous if the trench structure is selected from one or a combination of the following substructures: A) Partial structure with meandering course; B) Partial structure with an arched or S-shaped course; C) substructure with one or more local indentations; D) Partial structure with a conical shape.

[0015] It can be advantageous if the trench structure has a depth that corresponds to the thickness of the metal laminations and thus reaches down to the insulating body.

[0016] Further explanations of the invention, advantageous details and features, emerge from the following description of the Fig. 1 to 6 schematically illustrated embodiments of the invention, or of respective parts thereof.

[0017] The following directions apply to all figures: • x-direction: corresponds to the direction of the trench—the trench direction—as viewed from the edge of the insulating body. "Lengths" are determined parallel to this direction. • y-direction: corresponds to the perpendicular to the x-direction in a plane parallel to the second principal plane of the insulating body. Widths are determined parallel to this direction. • z-direction: corresponds to the normal direction of the insulating material body. "Depths" and "thicknesses" are determined parallel to this direction. Fig. 1 shows a plan view of a schematically illustrated substrate according to the invention. Fig. 2 shows a section of a first embodiment of a substrate according to the invention in plan view and two associated sectional views. Fig. 3 shows a section of a second embodiment of a substrate according to the invention in plan view and two associated sectional views. Fig. 4 shows a section of a third embodiment of a substrate according to the invention in plan view and two associated sectional views. Fig. 5 shows a section of a fourth embodiment of a substrate according to the invention in plan view and two associated sectional views. Fig. 6 shows various variants of a fifth embodiment of a substrate according to the invention in plan view.

[0018] Fig. Figure 1 shows a plan view of a schematically illustrated substrate 1 according to the invention for a power electronic circuit, which is manufactured using a pressure sintering process. Such substrates 1 typically comprise a flat insulating body 2, formed here from an industrial ceramic, for example and without limitation from aluminum oxide. Ceramics made of aluminum nitride and silicon nitride are also particularly common. This flat insulating body 2 has a thickness of 300 micrometers and an area of ​​150 square millimeters.

[0019] Metal laminations 3, formed from a metal layer—here, a copper layer—are arranged on the first main surface 20 of the insulating body 2. This copper layer is applied during the manufacture of the substrate 1 as a single layer, covering the entire area or only an edge region, and is then patterned. This patterning is preferably performed by wet-chemical etching.

[0020] The illustrated substrate 1 is divided into several regions. It has four central regions 100, each of which has a flat metal lamination 30. These regions are intended to form individual sub-substrates by dividing the substrate 1. On the non-visible, second main surface of these sub-substrates, conductor tracks are arranged that are essentially technically identical to the metal laminations 3 of the first main surface 20. These conductor tracks are designed to be populated with power electronic components and electrically connected, thus forming a conventional power electronic circuit. The pressure sintering process is ideally suited for forming the electrically conductive connection.

[0021] In order to separate the respective sub-substrates, the insulating material body 2 is weakened in the usual way, preferably by means of a laser beam, at predetermined breaking lines 202, 204, which are only partially shown, and then broken.

[0022] Furthermore, the first main surface 20 of the insulating body 2 has first and second partial laminations 4, 5 circumferentially surrounding the metal laminations 30 of the sub-substrates obtained after singulation, and also circumferentially on the edge region. These are produced together with the metal laminations 30 of the sub-substrates obtained after singulation and in the same way.

[0023] Typically, two of these partial laminations 4, 5 are used. A first and a second partial lamination 4, 5 are separated from each other by a trench 6. However, as described above, these trenches are particularly disadvantageous in a pressure sintering process.

[0024] Purely by way of example, a configuration of a dam 7 according to the invention is shown here, by which a residual layer 66 is formed from a trench 6 in one section. The dam material 70 of the dam 7 is formed as a second dam material 74, here an epoxy resin. Furthermore, purely by way of example, a conical trench structure 9 between two partial claddings is shown.

[0025] Basically, these partial laminations 4, 5 serve to stabilize the substrate 1 during the processing process and are only interrupted or form grooves 6 at the points where the aforementioned laser beam is intended to act on the insulating material body 2. On the other hand, the interruptions or grooves 6, as described above, are disadvantageous in the pressure-sintered connection because the sintering pad can penetrate into the grooves and become damaged there.

[0026] Fig. 2 shows a section of a first embodiment of a substrate 1 according to the invention in plan view, analogous to Fig. 1, and two corresponding sectional views along lines A and B. Shown is a corner section of the substrate 1 with a first and a second partial lamination 4, 5. The first partial lamination 4 is arranged on the narrow side in the edge region of the insulating body 2, cf. Fig. 1, while the second partial lamination 5 is arranged on the long side in the edge area of ​​the insulating body 2, see also Fig. 1. The trench 6, which is present between the two partial laminations 4, 5 in the prior art, is partially filled in this embodiment and forms a residual trench 66.

[0027] The dam material 70 for this purpose is a first dam material 72. This first dam material 72 is identical to the material of the partial claddings 4, 5, whereby a complete trench 6, as known from the prior art, was never actually formed. Rather, the trench 6 is not completely formed during the formation of the partial claddings 4, 5; instead, a residue of the metal layer, in this case the copper layer, remains between the two partial claddings 4, 5, so that only a residual trench 66 is actually formed. Both partial claddings 4, 5 are thus formed in one piece together with the first dam material 72 and are connected to one another.

[0028] In this embodiment, the outer edge 702 of the dam material 70 is directly aligned with the adjacent outer edge 402, 502 of the metal cladding 4, 5. Thus, viewed in the trench direction 600, no trench 6, nor any residual trench 66, is visible. Rather, the residual trench 66 exists on the side of the partial claddings 4, 5 facing the interior.

[0029] Viewed in the trench direction 600, the cross-sectional area 800 of the dam material 70, 72 is identical to the clear cross-sectional area 820 of the trench 6 or the remaining trench 66. Thus, the thickness of the first dam material 72 is also identical to the thickness of both adjacent partial claddings 4, 5. Furthermore, viewed in the trench direction 600, the length 802 of the dam material 70 is at least 50% of the clear depth 824 of the trench 6 or the remaining trench 66. With a clear depth of the trench 6 that corresponds to the thickness of the copper layer of the metal claddings 3 and thus also of the partial claddings 4, 5, which in this embodiment is 400 micrometers, the length 802 of the first dam material 72 must therefore be at least 200 micrometers.In order to avoid unnecessary disadvantages during the above-described laser processing of the first main surface 20 of the insulating material body 2, the length 802 of the first dam material 72 here is 30% of the length 822 of the trench 6, which here extends from the outer edge 702 to the end of the remaining trench 66 and amounts to 1.8 millimeters in this embodiment. The length 802 of the dam material 72 is thus 0.6 millimeters. Even shorter lengths 802 are of course advantageous. It must only be ensured that the dam material 70, 72 is not significantly deformed during the pressure application during the pressure sintering connection, which would in turn result in damage to the sintering pad.

[0030] Fig. Figure 3 shows a section of a second embodiment of a substrate 1 according to the invention in plan view and two associated sectional views along the lines A and B. This embodiment differs from that according to Fig. 2, on the one hand, in that the dam material 70 here is a second dam material 74, more precisely an epoxy resin, which was filled into the resulting continuous trench 6 after the structuring of the flat metal lamination 3 and the associated formation of the first and second partial laminations 4, 5. The second dam material 74 does not completely fill the trench 6 with respect to its depth 824, so that the maximum cross-sectional area 800 of the dam material here is 70% of the clear cross-sectional area 820 of the trench 6. The maximum cross-sectional area is considered here, i.e., the section of the second dam material 70, 74 that has the largest cross-section. This section lies in the middle of the trench section filled with the second dam material 74, viewed in the trench direction 600. In front of or behind it, the cross-sectional area is, of course, smaller for technical reasons - due to the filling with the epoxy resin.

[0031] On the other hand, this design differs from that according to Fig. 2 in that the outer edge 702 of the dam material 70, 74 is not aligned with the respective adjacent outer edges 402, 502 of the first and second partial cladding 4, 5. Rather, the outer edge 702 of the dam material 70, 74 is set back into the trench 6 by 5 times the clear depth 824 of the trench 6 relative to the adjacent outer edge 402, 502 of the first and second partial cladding 4, 5.

[0032] Fig. 4 shows a section of a third embodiment of a substrate 1 according to the invention in plan view and two associated sectional views along the lines A and B. In contrast to the embodiment according to Fig. 2, the first and second partial laminations 4, 5 are arranged on a common longitudinal side of the substrate 1. The other configurations of the first partial lamination 4, the first dam material 72 and the second partial lamination 5 are the same as those according to Fig. 2.

[0033] Furthermore, in contrast to the known prior art, here a respective outer edge 402, 502 of the metal laminations 4, 5 adjacent to the trench 6 is set back from the associated outer edge 22 of the insulating body 2 by only three times the thickness 824 of the partial laminations 4, 5. This overall prevents a significant undercut of the substrate 1 by the sintering pad during a sintering process within the framework of a pressure sintering process.

[0034] Fig. 5 shows a section of a fourth embodiment of a substrate 1 according to the invention in plan view and two associated sectional views along the lines A and B. In contrast to the embodiment according to Fig. 3, the first and second partial laminations 4, 5 are arranged on a common longitudinal side of the substrate 1, the respective outer edge 402, 502 of the first and second partial laminations 4, 5 adjacent to the trench 6 is thus aligned with the associated outer edge 22 of the insulating body 2. The other configuration of the first partial lamination 4 and the second partial lamination 5 is the same as that according to Fig. 2, whereby, however, the respective outer edge 402, 502 of the first and second partial laminations 4, 5 adjacent to the trench 6, here even the entire outer edge, is aligned with the associated outer edge 22 of the insulating body. This completely prevents the undercutting of the substrate 1 by the sintering pad in the region of the first and second partial laminations 4, 5 during a sintering process.

[0035] The second dam material 74 is formed here as a silicone rubber, which forms a drop-like cross-sectional area 800.

[0036] An ideal solution for the design of the first and second partial laminations 4, 5 and the dam material 70 thus results when both the outer edge 702 of the dam material 70 and the outer edges 402, 502 of the first and second partial laminations 4, 5 are aligned with the associated outer edge 22 of the insulating body 2. This prevents any undercutting of the substrate 1 by the sintering pad during a sintering process.

[0037] Fig. 6 shows various variants of a fifth embodiment of a substrate 1 according to the invention in a plan view. Seven variants of a trench 6 between two adjacent partial laminations are shown. The first variant I shows the prior art, i.e. a trench 6 whose cross-sectional area does not change over its entire length and is, in particular, rectangular, whereby the clear passage area 810 is identical to the clear cross-sectional area 820. This embodiment is further developed according to the invention in variants II to VII, wherein at least one side surface of the trench 6 does not have a rectilinear profile when viewed in the trench direction 600 and, in particular, in the projection onto the first main surface 20 of the insulating body 2.

[0038] Variant II shows an arcuate course, which can also be further developed into an S-shape, whereby the individual partial curvature radii can be designed as desired. The trench entrance 610 and the trench exit 620 are aligned as viewed in the trench direction 600. In this configuration, the clear passage area 810 is zero, since the indentation of the lower side of the trench 6 perpendicular to the trench direction 600 is larger than the width of the trench 6 at the trench entrance 610.

[0039] Variant III shows a curved course of the trench 6, which is formed by the fact that the trench inlet 610 and the trench outlet 620 are not aligned with each other when viewed in the trench direction 600. Rather, the trench inlet 610 and the trench outlet 620 are offset from each other by more than the trench width perpendicular to the trench direction 600. In this embodiment, the clear passage area 810 is again zero.

[0040] Variant IV shows a conical shape of trench 6, which diverges in the trench direction 600. The center of trench entrance 610 and the center of trench exit 620 are aligned with each other. This configuration results in a clear passage area 810, which is present here at trench entrance 610, which is smaller than half of the clear cross-sectional area 820, which is present here in particular at trench exit 620.

[0041] Variant V shows a course of the trench 6 with two indentations arranged opposite one another as viewed perpendicular to the trench direction 600. This configuration also results in a clear passage area 810 which is smaller than half of the clear cross-sectional area 820. In principle, such indentations can be formed alternatively or in addition to the configuration described here by means of a partially introduced dam material 70, comparable to the Fig. 3 and Fig.5. In this case, the dam material 70 would not completely cover the associated section of the first main surface 20 of the insulating body in the area of ​​the indentations, but only in the edge area of ​​the trench.

[0042] Variant VI shows a course of the trench 6 with a plurality of indentations arranged non-opposite each other, viewed perpendicular to the trench direction 600. This configuration again results in a clear passage area 810 that is smaller than half of the clear cross-sectional area 820.

[0043] Variant VII shows a trench 6 with a very simple meandering design. The meandering structure can, of course, also be more complex. This design results in a clear passage area 810 of one-third of the clear cross-sectional area 820.

Claims

[1] A substrate (1) divided into several areas with a plurality of central areas (100), each having a planar metal lamination and designed to form individual sub-substrates by dividing the substrate (1), for a power electronic circuit with a planar insulating body (2) and with planar metallic conductor tracks arranged on its second main surface and with planar metal laminations (3) arranged on its first main surface (20), and with partial laminations arranged around the metal lamination of the sub-substrates present after singulation and also around a perimeter area, wherein a first partial lamination (4) and a second partial lamination (5) thereof are arranged at or adjacent to an outer edge (22) of the insulating body (2) and wherein the two partial laminations (4,5) are at least partially separated from each other by a ditch (6) preferably extending to the first main surface (20) and wherein the ditch (6) either has a dam (7), wherein the ditch (6) is partially filled with a dam material (70), thus leaving a residual ditch (66), wherein the design of the dam material (70) satisfies the following conditions:, • viewed in the direction of the trench (600), the maximum cross-sectional area (800) of the dam material is at least 30% and at most 70% of the clear cross-sectional area (820) of the trench (6); • viewed in the direction of the trench (600), the length (802) of the dam material (70) is at least 50% of the clear depth (824) of the trench (6); or has a trench structure (9) in which the trench (6) has no or a clear passage area (810) of a maximum of 50% of the clear cross-sectional area (820) or has a mixed form of dam (7) and trench structure (9). [2] Substrate (1) according to claim 1, wherein the dam material (70), if present, is formed as a first dam material (72) which is identical to the material of the first and second partial laminations (4,5) and advantageously the two partial laminations (4,5) and the first dam material (72) are formed in one piece. [3] Substrate (1) according to claim 1, wherein the dam material (70), if present, is formed as a second dam material (74) which is different from the material of the first and second, completely separate, partial laminations (4, 5) and is either metallic or non-metallic, preferably as plastic. [4] Substrate (1) according to one of the preceding claims, wherein, viewed in the direction of the trench (600), the length (802) of the dam material, if any, (70) is a maximum of 50%, preferably a maximum of 30%, of the length (822) of the trench (6). [5] Substrate (1) according to any one of claims 1 to 4, wherein the outer edge (702) of the dam material (70), if present, is directly aligned with the adjacent outer edge (402,502) of the first and second partial lamination (4,5). [6] Substrate (1) according to one of claims 1 to 4, wherein the outer edge (702) of the dam material (70), if present, is set back into the trench (6) by a maximum of 10 times the clear depth (824) of the trench (6) relative to the adjacent outer edge (402, 502) of the two partial laminations (4, 5). [7] Substrate (1) according to any one of claims 1 to 6, wherein a respective outer edge (402, 502) of the two partial laminations (4, 5) adjacent to the trench (6) is aligned with the associated outer edge (22) of the insulating body (2). [8] Substrate (1) according to one of claims 1 to 6, wherein a respective outer edge (402, 502) of the two partial laminations (4, 5) adjacent to the trench (6) is set back a maximum of 10 times, in particular a maximum of 5 times, the thickness (824) of the two partial laminations (4, 5) relative to the associated outer edge (22) of the insulating body (2). [9] Substrate (1) according to claim 1, wherein the trench structure (9) is selected from one or a combination of the following substructures: A) Substructure with meandering course; B) Substructure with an arc- or S-shaped course; C) Substructure with one or more local indentations; D) Substructure with a conical shape. [10] Substrate (1) according to claim 1 or 9, wherein the trench structure (9) has a depth throughout that corresponds to the thickness (824) of the partial lamination (4,5).

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