Laser welding method

Abstract

A laser welding method using a laser welding jig having a plurality of pressing parts, includes a step of placing a second member on a first member; a step of pressing the second member with the plurality of pressing parts in a direction toward the first member to thereby form a gap between the first member and the second member at most 300 m; and a first welding step of laser-welding the first member and the second member by irradiating on a surface of the second member at a location between the pressing parts with laser light while conducting the step of pressing.

Claims

1. A laser welding method using a laser welding jig having a plurality of pressing parts, comprising: a step of placing a second member on a first member; a step of pressing the second member with the plurality of pressing parts in a direction toward the first member to thereby form a gap between the first member and the second member at most 300 m, the plurality of pressing parts being a pair of claws with an interval therebetween; a first welding step of laser-welding the first member and the second member by irradiating on a surface of the second member through the interval between the pair of claws with laser light while conducting the step of pressing; and a second welding step of laser-welding the first member and the second member by irradiating on the surface of the second member with the laser light while the pair of claws does not press the second member toward the first member.

2. The laser welding method according to claim 1, further comprising: a step of preparing a semiconductor device that comprises a ceramic insulated substrate, a front surface conductor pattern fixed on a front surface of the ceramic insulated substrate, a semiconductor chip electrically connected to the front surface conductor pattern, the first member electrically connected to the semiconductor chip, and the second member laser-welded to the first member at at least one portion to electrically connect thereto, and a step of sealing the ceramic insulated substrate, the front surface conductor pattern, the semiconductor chip, and a part of the first member with a sealing material before the step of placing the second member on the first member.

3. A laser welding method using a laser welding jig having a plurality of pressing parts, comprising a step of placing a second member on a first member; a step of inserting a spacer between the first and second members so that a gap between the first and second members is more than 0 m and at most 300 m, a step of pressing the second member with the plurality of pressing parts in a direction toward the first member to thereby form the gap between the first member and the second member at most 300 m, the plurality of pressing parts being a pair of claws with an interval therebetween; and a first welding step of laser-welding the first member and the second member by irradiating on a surface of the second member through the interval between the pair of claws with laser light while conducting the step of pressing, wherein in the first welding step, the laser is irradiated on the surface of the second member above the gap where the spacer is not inserted, to melt the first and second members and form a welded part, and a melted part of the first and second members enters into the gap to expand the welded part in a direction perpendicular to the direction toward the first member for increasing a shear strength of the welded part.

4. The laser welding method according to claim 3, further comprising a second welding step of laser-welding the first member and the second member at a region with a gap between the first member and the second member of at most 300 m after the first welding step.

5. The laser welding method according to claim 4, wherein a distance between centers of welding portions at the first and second welding steps is at most 4 mm.

6. The laser welding method according to claim 4, further comprising a step of forming engaging parts on the first member and the second member, for positioning the first member and the second member, wherein a portion of laser welding is different from the engaging parts.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIGS. 1A and 1B show a step in a laser welding method of the first embodiment of the present invention.

(2) FIGS. 2A and 2B show a step in a laser welding method following the steps of FIGS. 1A and 1B.

(3) FIGS. 3A and 3B show a step in a laser welding method following the steps of FIGS. 2A and 2B.

(4) FIGS. 4A and 4B show a step in a laser welding method following the steps of FIGS. 3A and 3B.

(5) FIGS. 5A, 5B, and 5C show a construction of an essential part of a laser welding jig of the second embodiment of the present invention.

(6) FIG. 6 is a sectional view showing an assembling step of a semiconductor device that is the third embodiment of the present invention.

(7) FIG. 7 is a sectional view showing an assembling step following the step of FIG. 6 of the semiconductor device.

(8) FIG. 8 is a sectional view showing an assembling step following the step of FIG. 7 of the semiconductor device.

(9) FIG. 9 is a sectional view showing an assembling step following the step of FIG. 8 of the semiconductor device.

(10) FIGS. 10A, 10B, and 10C are enlarged views of the part where the upper emitter terminal is put overlapped on the lower emitter terminal, each terminal having an engaging part.

(11) FIG. 11 shows a relationship between a gap between terminals and shear strength of the joined part.

(12) FIGS. 12A, 12B, and 12C show a relationship between the gap between the terminals and the configuration of the welded part.

(13) FIG. 13 shows a sputtered particle generated in the case without resin sealing.

(14) FIG. 14 is a sectional view of an essential part of a semiconductor device of the fourth embodiment of the present invention.

(15) FIG. 15 shows a construction of a power semiconductor module of a general type.

DETAILED DESCRIPTION OF THE INVENTION

(16) Some preferred embodiments of the present invention will be described in detail in the following with reference to the accompanying drawings.

First Embodiment

(17) FIGS. 1A and 1B through FIGS. 4A and 4B show a laser welding method according to the first embodiment of the present invention in the sequence of the laser welding method. FIGS. 1A, 2A, 3A, and 4A are plan views and FIGS. 18, 2B, 38, and 4B are sectional views cut along the line Y-Y in FIGS. 1A, 2A, 3A, and 4A, respectively.

(18) Referring to FIGS. 1A and 1B, a second member at the upper position, which is a second member 2 to be welded, is placed on a first member at the lower position, which is a first member 1 to be welded, with the first and second members overlapping each other. A gap 10 between the two members 1 and 2 to be welded can be larger than 300 m in some cases. The first and second members 1 and 2 to be welded are composed of a high thermal conductivity material exhibiting a thermal conductivity of at least 100 W/(m.Math.K). The material can be selected from copper (Cu), a copper-molybdenum (CuMo) alloy, a copper-tungsten (CuW) alloy, molybdenum (Mo), tungsten (W), an aluminum-silicon carbide (AlSiC) alloy, and a silicon-silicon carbide (SiSiC) alloy, for example. The surface of the second member 2 to be welded on which laser light is irradiated is preferably plated with electroless nickel-phosphorus (NiP) plating, electroless nickel-boron (NiB) plating, or electrolytic nickel (Ni) plating, for example. The plating is favorable because it exhibits improved absorption coefficient of laser light.

(19) Then as shown in FIGS. 2A and 2B, a support column 40 of a laser welding jig 100 is pressed by a pressing device such as a pneumatically driven cylinder (not shown in the figure), for example. The laser welding jig 100 is moved to such a position that a welding part 5 (indicated in FIGS. 3A and 3B) falls between two claws 39, which are pressing parts, formed at the tip of the support column 40. The laser welding jig presses the second member 2 to be welded with a force 4 of about 39.8 N to make the gap 10 between the two members 1 and 2 to be welded be at most 300 m. The pair of claws 39 is provided for making the gap 10 between the first and second members to be welded be sufficiently small in the overlapped state. The places of the claws that contact the second member 2 to be welded is a straight line with a length L of about 1 mm. In FIGS. 2A and 2B, the two contact places are aligned on a common straight line, but they can be arranged in parallel facing each other.

(20) Then as shown in FIGS. 3A and 3B, an irradiation surface 6 is irradiated with laser light 35 to execute laser welding. The laser light 35 has a pulse waveform. The pair of claws 39 keeps its configuration until the welded place solidifies. The welded place cools down and solidifies rapidly through heat diffusion toward the welded members 1 and 2 in the surroundings.

(21) If there are two or more welding places, as shown in FIGS. 4A and 4B, after a first laser welding has finished, the pair of claws 39 is moved to a different place from the welded part 5 of first laser welding, and laser welding is conducted at a place next to the first welded part 5. Laser welding of second and thereafter are carried out without pressing the second member 2 to be welded with the pair of claws 39. Because the gap between the two members 1 and 2 has fixed to be not larger than 300 m during the first laser welding, the laser welding of second and thereafter does not need to press the second member 2 to be welded with the pair of claws 39. Places of laser welding of second and thereafter can be any place as long as the gap between the two members 1 and 2 to be welded is ensured at a distance not larger than 300 m.

(22) According to the welding procedure, the step of pressing by the pair of claws 39 can be eliminated in laser welding of second and thereafter. Thus, a dead time can be shortened. When the places of laser welding of second and thereafter are set at a vicinity of within 2 mm from the first laser welding place, the distance between welded places 5 is sufficiently small, enhancing joint strength.

(23) Laser welding can of course be conducted by pressing with the pair of claws 39 after moving the pair of claws 39 and the laser light 35 together.

(24) Laser welding can be favorably carried out when the thickness of the first member 1 to be welded, which corresponds to the lower emitter terminal 30 in FIG. 7, is at least 0.5 m, and the thickness of the second member 2 to be welded, which corresponds to the upper emitter terminal 33 in FIG. 8, is at most 1 mm. If the thickness of the first member 1 to be welded is less than 0.5 mm, the welded place of the first welded member may be punched through to the back surface. If the thickness of the second member 2 to be welded is larger than 1 mm, the welded part does not sufficiently penetrate into the first welded member, lowering the welding strength. If the output power of the laser light is enhanced too high in the intention of increasing of the welding strength, larger heat is conducted to the claws 39, resulting in deformation of the claws.

(25) The distance between centers of laser welded parts is desirably not larger than 4 mm. If the distance is larger than 4 mm, the joining strength between the first member and the second member tends to decrease.

Second Embodiment

(26) FIGS. 5A, 5B, and 5C show a construction of an essential part of a laser welding jig 100 according to the second embodiment of the present invention, in which FIG. 5A is a perspective view of the whole structure, FIG. 5B is a side view of a pair of claws 39, and FIG. 5C is a front view of the pair of claws 39.

(27) The laser welding jig comprises a support column 40 and two claws 39 facing each other and connected to the support column 40. The pair of claws 39 pushes the both ends of an area of a welding part. The edges of the pair of claws are linear like a knife edge, but blunt. The pair of claws 39 depicted in FIGS. 5A, 5B, and 5C has linear edges in the direction 90 degrees-revolved in the horizontal direction with respect to the direction of extension of the claws 39. But the claws can be arranged in the direction rotated by 90 degrees from the direction depicted in FIGS. 5A, 5B, and SC.

(28) As shown in FIG. 3A, the distance T between the two claws 39 is wide enough not to interfere with laser light 35 and wider than the size of the welded part 5 that is a mark of fusion solidified after melted by the laser light 35. More specifically, when the irradiation area 6 by the laser light 35 is 0.4 mm in diameter D1, the diameter D2 of the welded part 5 is about 1.5 mm. Separating each of the claws 39 from the welded part 5 by a distance in the range from 0.5 mm to 3 mm, the interval T between the two claws 39 becomes 2.5 mm to 7.5 mm. The dimensions in these ranges are favorable because the pair of claws 39 does not interfere with the laser light 35, which means the laser light 35 does not irradiate the claws, and the welded part 5 does not contact the claws 39. The laser light 35 irradiates the place between the two claws 39. The locations pressed by the claws 39 are in the vicinity of the irradiation area 6 of the laser light 35, and the two claws 39 press the vicinity of the region to become the welded part 5 of the second member 2 to be welded to make the gap between the member 1 to be welded and the member 2 to be welded be at most 300 m. In this arrangement, the laser light 35 irradiates the area between the two claws 39 to laser-weld the welding members 1 and 2.

(29) If the interval T between the two claws 39 is too wide, the first member 1 to be welded and the second member 2 to be welded are insufficiently close contacting each other and the gap 10 between the two members is wider than 300 m, lowering the joining strength of the welded part 5. Use of the laser welding jig 100 allows to press the vicinity of the welding part 5 and to narrow the gap 10 between the members 1 and 2 to be welded within 300 m achieving a stable joint condition.

Third Embodiment

(30) FIGS. 6 through 9 show a procedure of assembling a semiconductor device 200 that is the third embodiment of the present invention, and are sectional views showing assembling steps given in the sequence of the steps. These figures show assembling steps of a semiconductor device in which a wiring terminal on a semiconductor chip is joined with an externally leading out terminal by means of laser welding. In the assembling steps, the laser welding method described previously is applied.

(31) Referring to FIG. 6, a semiconductor device 200 comprises a DCB substrate 24 having a rear surface conductor pattern 23 disposed on a heat radiating base 21 made of a high thermal conductivity material, for example copper or aluminum, intercalating a joining material 22 such as solder between them. In the procedure of assembling the semiconductor device 200, a semiconductor chip 27 and a collector terminal 31 are arranged on a front surface conductor pattern 25 formed on the surface of the DCB substrate 24 through joining materials 26 and 29, respectively, such as solder. Then, a lower emitter terminal 30 is arranged on a main electrode surface (not depicted) of the semiconductor chip 27 through a joining material 28. This lower emitter terminal 30 is a wiring terminal having a thickness of about 1.5 mm, for example. After heated to melt, the joining materials 22, 26, 28, and 29 are cooled dad solidified to provide a monolithic body including the above mentioned components. The semiconductor chips 27 can be an insulated gate bipolar transistor (IGBT) and a free-wheeling diode (FWD) chip. The semiconductor chips 27 are electrically connected to the lower emitter terminal 30 through the joining material 28. The lower emitter terminal 30 is a wiring terminal, which is a first member or a first member to be welded, and made of a material, for example copper, exhibiting high electric conductivity and high thermal conductivity. The DCB substrate 24 is composed of a ceramic insulated substrate 24a, which is an insulated substrate made of ceramic, and a rear surface conductor pattern 23 and a front surface conductor pattern 25.

(32) Then, as shown in FIG. 7, the components assembled to a state of FIG. 6 are sealed with a resin sealing material 32. The resin sealing material 32 can be an epoxy resin. The components are surrounded by a wall arranged at the periphery of the heat radiating base 21 and sealed with liquid state epoxy resin. The resin is cured to seal the components. Here, the upper surface of the lower emitter terminal 30 and the upper part of the collector terminal 31 are not sealed and are remaining exposed to the air. The semiconductor chips 27 and the joining material 28 are sealed with the resin.

(33) The resin sealing material 32 seals the upper surface of the heat radiating base 21, the DCB substrate, the semiconductor chip 27, and the front surface conductor pattern 25. The surface 32a of the resin sealing material 32 is disposed not to contact the rear surface 30a of the lower emitter terminal 30. If the surface 32a of the resin sealing material 32 is contacting the rear surface 30a of the lower emitter terminal 30, the heat dissipation from the rear surface 30a of the lower emitter terminal 30 in the laser welding process is restricted, which expands the melted region and the melted region may unfavorably penetrate through the lower emitter terminal 30.

(34) The step of resin sealing can be omitted in the case of rare sputtering particles in the laser welding process.

(35) Then as shown in FIG. 3, an upper emitter terminal 33 is put overlapping on the lower emitter terminal 30 indicated in FIG. 7. The upper emitter terminal 33 is an externally leading out terminal, which is a second member or a second member to be welded. The thickness of the upper emitter terminal 33 is 1.0 mm, for example. At this stage, the gap 10 between the upper and lower emitter terminals 30 and 33 may be larger than 300 m. The upper emitter terminal 33 is made of a material, for example copper, exhibiting high electrical conductivity and high thermal conductivity. The surface of the upper emitter terminal 33 is plated with electrolytic nickel, for example.

(36) Then as shown in FIG. 9, the surface of the upper emitter terminal 33 is pressed with a pair of claws 39 of a laser welding jig 100 to make the gap 10 between the upper and lower emitter terminals 30 and 33 be at most 300 m. Subsequently, laser light irradiates the surface of the upper emitter terminal 33 between the two claws 39 to conduct laser welding of the upper emitter terminal 33 and the lower emitter terminal 30. When second laser welding is conducted at a nearby place, the gap 10 between the upper emitter terminal 33 and the lower emitter terminal 30 has already been made at a dimension not larger than 300 m. Thus, the surface of the upper emitter terminal 33 is not necessarily pressed with the pair of claws 39, although the laser welding can be conducted while pressing the upper emitter terminal 33 with the pair of claws 39.

(37) The distance between the outer peripheries of laser welded places is preferably at most 2 mm. If the distance is larger than 2 mm, the gap between the first member and the second member is liable to increase, which decreases the joining strength of the first and second members.

(38) FIGS. 10A, 10B, and 10C are enlarged views of the place where the upper emitter terminal 33, a second member, and the lower emitter terminal 30, a first member, are put overlapping with each other, in which FIG. 10A is a sectional view of the upper emitter terminal 33 having a protruding part 36 and the lower emitter terminal 30 having a recessed part 37, FIG. 10B is a sectional view showing the protruding part 36 of the upper emitter terminal 33 is engaged with the recessed part 37 of the lower emitter terminal 30, and FIG. 10C is a sectional view showing the laser welding process while the upper emitter terminal 33 is pressed by the pair of claws 39. The protruding part 36 formed on the upper emitter terminal 33 and the recessed part 37 formed on the lower emitter terminal 30 allows positioning of the upper emitter terminal 33, avoiding positional shift of the emitter terminals in the assembling process.

(39) In order to reduce the gap 10 between the emitter terminals 30 and 33, the surface of the upper emitter terminal 33 is pressed with the pair of claws 39 of the laser welding jig 100, and laser light irradiates the upper emitter terminal 33 in the configuration with the gap 10 between the upper emitter terminal 33 and the lower emitter terminal 30 disposed under the upper emitter terminal 33 being at most 300 m. Thus, a good welded part 34 is obtained.

(40) FIG. 11 shows a relationship between the gap 10 between the emitter terminals 30 and 33 and shear strength of the welded part 34. An upper emitter terminal 33 and a lower emitter terminal 30 are disposed overlapping with each other intercalating a spacer between the terminals. Laser welding is conducted in this configuration in which the gap 10 between the emitter terminals 30 and 33 is controlled by the spacer. FIG. 11 shows shear strength in terms of normalized value with reference to the value in the condition of direct close contact, which means without a gap. The shear strength here is a tensile strength when the terminals 30 and 33 are pulled in the longitudinal direction, and represents a joint strength of the welded part 34.

(41) FIG. 11 shows that the shear strength is larger than the one in the case of no gap when the gap 10 between the terminals 30 and 33 is in the range of up to 300 m. At the gap of 400 m, the shear strength decreased by about 30% as compared with the case of no gap, and at the gap of 500 m, laser welding becomes impossible. In order to obtain a shear strength larger than the value in the case of direct contact, which means no gap, the gap between the terminals 30 and 33 needs to be at most 300 m. It has been demonstrated that a shear strength larger than the one in the case of direct contact can be readily obtained by laser welding using the laser welding jig 100 of the invention as shown in FIGS. 5A, 5B, and 5C.

(42) A gap larger than 300 m causes adverse effect of increased heat resistance at the welded part 34 as well as decrease in the shear strength. Therefore, the gap between the terminals 30 and 33 is necessarily at most 300 m.

(43) FIGS. 12A, 12B, and 12C show relationship between the gap 10 between the terminals 30 and 33 and the configuration of the welded part 34, in which FIG. 12A is a sectional view without gap 10 between the terminals 30 and 33, FIG. 12B is a sectional view with the gap 10 between the terminals 30 and 33 not larger than 300 m, and FIG. 12C is a sectional view with the gap 10 between the terminals 30 and 33 larger than 300 m.

(44) Referring to FIG. 12A, in the case of no gap, which is a direct contact case, the welded part 34a cannot expand at the boundary 49 between the terminals 30 and 33.

(45) Referring to FIG. 12B, in the case the gap between the terminals 30 and 33 is not larger than 300 m, the welded part expands at the gap, increasing the area of the welded part 34b. As a consequence, the shear strength becomes larger than the case of no gap.

(46) Referring to FIG. 12C, when the gap 10 between the terminals 30 and 33 exceeds 300 m, the welded part 34c at the gap 10 shrinks in the center portion of the welded part, and thus, the shear strength is lowered.

(47) FIG. 13 shows scattering of sputtered metallic particles 42 in the laser welding process without resin sealing. The sputtered particles 42 attach onto the semiconductor chip 27 and the front surface conductor pattern 25, which may cause failure of electric insulation. This failure can be avoided by sealing the semiconductor chip 27 with a resin up to the level of joining material 28.

(48) Stable joining strength is ensured by pressing the upper emitter terminal 33 using the laser welding jig 100 of the invention to make the gap between the upper emitter terminal 33 and the lower emitter terminal 30 be at most 300 m, and joining the lower emitter terminal 30 and the upper emitter terminal 33 according to the laser welding method of the invention.

(49) The lower emitter terminal 30 and the upper emitter terminal 33 are made of a high thermal conductivity material exhibiting a thermal conductivity of at least 100 W/(m.Math.K). Preferable materials include: copper (Cu), a copper-molybdenum (CuMo) alloy, a copper-tungsten (CuW) alloy, molybdenum (Mo), tungsten (W), an aluminum-silicon carbide (AlSiC) alloy, and a silicon-silicon carbide (SiSIC) alloy, for example.

(50) The thickness of the lower emitter terminal 30 is preferably at least 0.5 mm, and the thickness of the upper emitter terminal 33 is at most 1 mm. If the thickness of the lower emitter terminal 30 less than 0.5 mm causes the laser welded part penetrates through the lower emitter terminal 30. The thickness of the lower emitter terminal 30 is more preferably, not smaller than 0.8 mm.

(51) The thickness of the upper emitter terminal 33 thicker than 1 mm increases the proportion of the energy of laser welding consumed in the upper emitter terminal 33 and decreases the proportion of the energy consumed in the lower emitter terminal 30. As a consequence, the area of melted part of the lower emitter terminal decreases resulting in lowered shear strength.

(52) Both of the lower emitter terminal 30 and the upper emitter terminal 33, or only the upper emitter terminal 33, which is irradiated by laser light is preferably plated with a material that absorbs much energy of laser light. Preferable plating includes electroless nickel-phosphorus (NiP) plating, electroless nickel-boron (NiB) plating, and electrolytic nickel (Ni) plating, for example. The plating is favorable because it improves absorption coefficient of laser light.

Fourth Embodiment

(53) FIG. 14 is a sectional view of an essential part of a semiconductor device 200 according to the fourth embodiment of the present invention. The semiconductor device 200 is manufactured according to the laser welding method of the first embodiment and using the laser welding jig 100 of the second embodiment.

(54) The semiconductor device 200 comprises a heat radiating base 21, a DCB substrate 24 having a rear surface conductor pattern 23 that is fixed through a joining material 22 such as solder to the heat radiating base 21, and a semiconductor chip 27 fixed to a front surface conductor pattern 25 through a joining material 26 such as solder. The DCB substrate 24 is composed of a ceramic insulated substrate 24a, a rear surface conductor pattern 23 fixed on the rear surface of the ceramic insulated substrate 24a, and a front surface conductor pattern 25 fixed on the front surface of the ceramic insulated substrate 24a. The semiconductor device 200 further comprises a lower emitter terminal 30 fixed to the surface electrode of the semiconductor chip 27 through a joining material 28 such as solder, an upper emitter terminal 33 fixed to the lower emitter terminal by means of laser welding, and a collector terminal 31 fixed to the front surface conductor pattern 25 through a joining material 29 such as solder. The semiconductor device 200 also comprises a resin sealing material 32 that seals the whole device excepting the side face and rear face of the heat radiating base 21, the front surface of the lower emitter terminal 30, a tip portion of the collector terminal 31, and the upper emitter terminal 33, which are exposed to the air.

(55) A high shear strength is obtained by ensuring the gap 10 between lower emitter terminal 30 and the upper emitter terminal 33 to be within 300 m. Positional shift of the upper emitter terminal 33 in assembling process of the semiconductor device 200 is avoided by forming a recessed part 37 on the lower emitter terminal 30 and a protruding part 36 on the upper emitter terminal 33 and positioning a welding place of the terminals 30 and 33 with the aid of the protruding part and the recessed part. Alternatively, positional shift of the upper emitter terminal 33 in assembling process of the semiconductor device 200 is likewise avoided by forming a protruding part on the lower emitter terminal 30 and a recessed part on the upper emitter terminal 33 and positioning a welding place of the terminals 30 and 33 with the aid of the protruding part and the recessed part. The recessed part can be a through hole.

(56) In some cases in the semiconductor device 200, two linear compression marks with a length of about 1 mm may be formed on the upper emitter terminal 33 at two places on either side of the welded part 34.

DESCRIPTION OF SYMBOLS

(57) 1: first welded member, first member 2: second welded member, second member 4: force 5, 34: welded part 6: irradiated surface 10: gap 21, 51: heat radiating base 22, 26, 28, 29, 52, 56: joining material 23, 53: rear surface conductor pattern 24, 54: DCB substrate 24a, 54a: ceramic insulated substrate 25, 55: front surface conductor pattern 27, 57: semiconductor chip 30: lower emitter terminal, first member 30a: rear surface 31: collector terminal 32: resin sealing material 32a: front surface 33: upper emitter terminal, second member 35: laser light 36 protruding part 37: recessed part 39: claw, pressing part 40: support column 42: sputtered particle 49: boundary region 58: terminal-inserted type resin casing 59, 60, 61: terminal 62: bonding wire 63: gel sealing material 100: laser welding jig 200: semiconductor device 500: power semiconductor module D1, D2: diameter L: length T: interval