Semiconductor device
09536875 ยท 2017-01-03
Assignee
Inventors
Cpc classification
H10D12/481
ELECTRICITY
H10D62/142
ELECTRICITY
H10D62/127
ELECTRICITY
International classification
H01L27/06
ELECTRICITY
H01L29/06
ELECTRICITY
H01L29/10
ELECTRICITY
H01L29/66
ELECTRICITY
H01L29/739
ELECTRICITY
Abstract
An IGBT is disposed in an IGBT portion, and an FWD is disposed in an FWD portion. A p-type base region and an n.sup.-type drift region are alternately exposed in a trench longitudinal direction in a substrate front surface in a mesa portion between neighboring trenches in the IGBT portion. A p-type anode region and the n.sup.-type drift region are alternately exposed in the trench longitudinal direction in the substrate front surface in a mesa portion in the FWD portion, and a repetitive structure is formed with a portion of the n.sup.-type drift region sandwiched between p-type anode regions and one p-type anode region in contact with the portion as one unit region. The proportion occupied by the p-type anode region in one unit region (an anode ratio) () is 50% to 100%.
Claims
1. A semiconductor device comprising a first element region in which an insulated gate bipolar transistor is provided and a second element region in which a diode is provided on a semiconductor substrate that forms a first conductivity type drift region, the semiconductor device further comprising: a plurality of trenches provided in stripe form extending in a trench longitudinal direction perpendicular to a direction in which the first element region and second element region are aligned from the first element region across the second element region in a front surface of the semiconductor substrate; a gate insulating film provided along side walls and bottom surfaces of the trenches; a gate electrode provided on an inner side of the gate insulating film inside the trenches; a second conductivity type base region selectively provided in a mesa portion between neighboring trenches of the first element region; a second conductivity type anode region selectively provided in the mesa portion between neighboring trenches of the second element region; a first conductivity type emitter region selectively provided inside the base region; a first electrode in contact with the base region, emitter region, and anode region; a second conductivity type collector region provided on a back surface of the semiconductor substrate in the first element region; a first conductivity type cathode region provided on the back surface of the semiconductor substrate in the second element region; and a second electrode in contact with the collector region and cathode region, wherein the anode region and drift region are repeatedly, alternately disposed in the trench longitudinal direction in a top surface of the mesa portion between neighboring trenches of the second element region.
2. The semiconductor device according to claim 1, wherein built-in depletion layers spreading into the mesa portion from each of neighboring anode regions are linked to each other.
3. The semiconductor device according to claim 1, wherein the first electrode is further in contact with the drift region in the second element region, and a proportion occupied by the anode region of a unit region formed of the anode region and the drift region in a portion sandwiched by the anode region and the anode region neighboring the anode region in the trench longitudinal direction is less than 50%.
4. The semiconductor device according to claim 3, wherein the drift region and the first electrode form a Schottky junction.
5. A semiconductor device comprising: an insulated gate bipolar transistor (IGBT) region; a diode region adjacent to the IGBT region; wherein the diode region includes parallel trenches and a repeating pattern of an anode region alternating with a drift region on a surface between the parallel trenches, and a unit region in the diode region is defined as an anode region and an adjacent drift region on the surface between the parallel trenches.
6. A semiconductor device according to claim 5, wherein a first electrode is in contact with the drift region in the diode region, and an anode ratio, defined as a ratio of a dimension of the anode region of the unit region to a dimension of the unit region as a whole, is less than 50%.
7. The semiconductor device of claim 6, wherein an anode region and a drift region are connected to a common emitter electrode.
8. The semiconductor device according to claim 1, wherein the drift region in the top surface of the mesa portion is covered by an insulator film, and a proportion occupied by the anode region of a unit region formed of the anode region and the drift region in a portion sandwiched by the anode region and the anode region neighboring the anode region in the trench longitudinal direction is 50% or more and less than 100%.
9. The semiconductor device of claim 5, wherein the drift region between the surface of the parallel trenches is covered by an insulator film, and an anode ratio, defined as a ratio of a dimension of the anode region of the unit region to a dimension of the unit region as a whole, is 50% or more and less than 100%.
10. The semiconductor device of claim 7, wherein the drift region and the first electrode form a Schottky junction.
11. The semiconductor device of claim 9, wherein the anode ratio is between substantially 50% and substantially 75%.
12. The semiconductor device of claim 9, wherein the anode ratio is substantially 75%.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION
(41) Hereafter, referring to the attached drawings, a detailed description will be given of preferred embodiments of a semiconductor device according to the invention. A layer or region being prefixed by n or p in the specifications or attached drawings means that electrons or holes respectively are majority carriers. Also, + or attached to n or p indicates a higher impurity concentration or lower impurity concentration respectively than in a layer or region to which neither is attached. In the following description of the embodiments and in the attached drawings, the same reference signs are given to the same configurations, and redundant descriptions are omitted.
(42) (Embodiment 1)
(43) A description will be given of the configuration of a semiconductor device according to Embodiment 1.
(44) The FWD of the FWD portion 22 is connected in anti-parallel to the IGBT of the IGBT portion 21. That is, the semiconductor device according to Embodiment 1 is a reverse conducting IGBT (RC-IGBT). A multiple of a trench 2 are provided at predetermined intervals in a stripe form extending in a direction (the longitudinal direction) perpendicular to the direction in which the IGBT portion 21 and FWB portion 22 are aligned (the lateral direction), from the IGBT portion 21 across the FWB portion 22, on the front surface of the n.sup.-type semiconductor substrate.
(45) A gate insulating film 3 is provided inside the trench 2 along the inner wall of the trench 2. Also, a gate electrode 4 is provided on the inner side of the gate insulating film 3 inside the trench 2. In the IGBT portion 21, a p-type base region 5-1 is provided at predetermined intervals in the trench 2 longitudinal direction in a mesa portion between neighboring trenches 2. The p-type base region 5-1 is provided so as to be in contact with the trench 2, and to a depth (a depth from the substrate front surface) less than that of the trench 2.
(46) That is, in the IGBT portion 21, the p-type base region 5-1 and n.sup.-type drift region 1 are alternately exposed in the trench 2 longitudinal direction on the front surface of the n.sup.-type semiconductor substrate. A width x11 in the trench 2 longitudinal direction of the p-type base region 5-1 is greater than the width in the trench 2 longitudinal direction of a portion of the n.sup.-type drift region 1 sandwiched by the p-type base region 5-1, that is, a first pitch (disposition interval) x12 in the trench 2 longitudinal direction of the p-type base region 5-1 (x11>x12). An n.sup.+-type emitter region 6 and a p.sup.+-type contact region 7 are selectively provided inside the p-type base region 5-1.
(47) The n.sup.+-type emitter region 6 is in contact with the gate insulating film 3 provided on the side walls of the trench 2, and opposes the gate electrode 4 across the gate insulating film 3. The n.sup.+-type emitter region 6 is formed of, for example, a first n.sup.+-type region 6-1, provided on the side of each trench 2 sandwiching the p-type base region 5-1, and a second n.sup.+-type region 6-2 provided between first n.sup.+-type regions 6-1 and linking the first n.sup.+-type regions 6-1. The trench 2 longitudinal direction width of the second n.sup.+-type region 6-2 is, for example, less than the trench 2 longitudinal direction width of the first n.sup.+-type region 6-1, whereby the n.sup.+-type emitter region 6 has, for example, an H-shaped planar form.
(48) The p.sup.+-type contact region 7 is provided between first n.sup.+-type regions 6-1, and in contact with the n.sup.+-type emitter region 6. In this way, the IGBT portion 21 on the front surface side of the n.sup.-type semiconductor substrate is of a structure wherein, with the p-type base region 5-1 disposed thinned out, a trench gate type MOS gate structure formed of the trench 2, gate insulating film 3, gate electrode 4, p-type base region 5-1, n.sup.+-type emitter region 6, and p.sup.+-type contact region 7 is repeatedly disposed in the trench 2 longitudinal direction. Each MOS gate configures an IGBT (cell portion).
(49) In the FWD portion 22, the trench 2 of the FWD portion 22 is also of a trench gate structure, in the same way as the trench 2 of the IGBT portion 21, in order to simplify the manufacturing process by unifying the wiring layout in the IGBT portion 21 and FWD portion 22. In the FWD portion 22, a p-type anode region 5-2 is provided at predetermined intervals in the trench 2 longitudinal direction in a mesa portion between neighboring trenches 2. That is, the p-type anode region 5-2 and n.sup.-type drift region 1 are alternately exposed in the trench 2 longitudinal direction on the front surface of the n.sup.-type semiconductor substrate.
(50) In this way, a p-type base region provided in a mesa portion between neighboring trenches 2 in the FWD portion 22 configures the p-type anode region 5-2. A p.sup.+-type contact region may be provided inside the p-type anode region 5-2. Hereafter, a description will be given with a case wherein no p.sup.+-type contact region is formed in the FWD portion 22 as an example. The p-type anode region 5-2 is provided in contact with the trench 2, and to a depth less than that of the trench 2. The impurity concentration of the p-type anode region 5-2 may be equal to the impurity concentration of the p-type base region 5-1, or may be lower than the impurity concentration of the p-type base region 5-1.
(51) The FWD portion 22 on the front surface side of the n.sup.-type semiconductor substrate is of a structure such that the p-type anode region 5-2 is repeatedly disposed in the trench 2 longitudinal direction, wherein each p-type anode region 5-2 configures an FWD (cell portion). Specifically, a repetitive structure wherein a portion of the n.sup.-type drift region 1 sandwiched by p-type anode regions 5-2 neighboring in the trench 2 longitudinal direction (hereafter referred to as a portion of the n.sup.-type drift region 1 sandwiched by the p-type anode region 5-2), and one p-type anode region 5-2 in contact with this portion, is taken to be one unit (hereafter referred to as a unit region) is formed in a mesa portion between neighboring trenches 2. A description will be given hereafter of a proportion (hereafter referred to as an anode ratio) of one unit region occupied by the p-type anode region 5-2. It is good when a width w10 in the trench 2 longitudinal direction of the p-type anode region 5-2 is, for example, greater than a width (that is, mesa width) w20 in the trench 2 lateral direction of the mesa portion. The reason for this is that the anode ratio is easily set within a preferred range to be described hereafter.
(52) The front surface of the n.sup.-type semiconductor substrate is covered with an interlayer dielectric 8 having first and second contact holes 8-1 and 8-2. The first contact hole 8-1 is provided in each cell portion of the IGBT portion 21, and the n.sup.+-type emitter region 6 and p.sup.+-type contact region 7 of one cell portion are exposed in one first contact hole 8-1. The second contact hole 8-2 is provided in each cell portion of the FWD portion 22, and the p-type anode region 5-2 of one cell portion is exposed in one second contact hole 8-2. The n.sup.-type drift region 1 is not exposed in the first and second contact holes 8-1 and 8-2.
(53) It is preferable that an aperture width w11 in the trench 2 longitudinal direction of the second contact hole 8-2 and an aperture width w21 in the trench 2 lateral direction of the second contact hole 8-2 are of a size such that practically the whole of the p-type anode region 5-2 can be exposed. The reason for this is that contact resistance can be reduced, and on-state voltage can thus be reduced. Specifically, taking deviation in the alignment of an etching mask for forming the second contact hole 8-2 into consideration, it is good when the aperture width w11 in the trench 2 longitudinal direction of the second contact hole 8-2 and aperture width w21 in the trench 2 lateral direction of the second contact hole 8-2 are slightly smaller than the width w10 in the trench 2 longitudinal direction of the p-type anode region 5-2 and the width (mesa width w20 between trenches 2) in the trench 2 lateral direction of the p-type anode region 5-2 respectively.
(54) More specifically, the aperture width w11 in the trench 2 longitudinal direction of the second contact hole 8-2 may be reduced so that both end portions in the trench 2 longitudinal direction of the second contact hole 8-2 are positioned a width w12 (in the region of, for example, 0.5 m to 1.0 m) to the inner side of the p-type anode region 5-2 from the boundary between the p-type anode region 5-2 and n.sup.-type drift region 1. The aperture width w21 in the trench 2 lateral direction of the second contact hole 8-2 may be reduced so that both end portions in the trench 2 lateral direction of the second contact hole 8-2 are positioned a width w22 (in the region of, for example, 0.5 m to 1.0 m) to the inner side of the p-type anode region 5-2 from the boundary between the p-type anode region 5-2 and the inner wall of the trench 2.
(55) An emitter electrode 9 is in contact with the n.sup.+-type emitter region 6 and p.sup.+-type contact region 7 via the first contact hole 8-1. Also, the emitter electrode 9, doubling as an anode electrode, is in contact with the p-type anode region 5-2 via the second contact hole 8-2. The emitter electrode 9 is electrically isolated from the gate electrode 4 by the interlayer dielectric 8. A p.sup.+-type collector region 11 is provided in the IGBT portion 21, and an n.sup.+-type cathode region 12 provided in the FWD portion 22, in a surface layer of the n.sup.-type semiconductor substrate back surface.
(56) An n-type buffer layer 10 is provided between the p.sup.+-type collector region 11 and n.sup.+-type cathode region 12 and the n.sup.-type drift region 1. The n-type buffer layer 10 has a function as an n-type field stop layer that restricts so that a depletion layer spreading from the p-n junctions between the p-type base region 5-1 and p-type anode region 5-2 and the n.sup.-type drift region 1 when in an off-state does not reach the p.sup.+-type collector region 11. A collector electrode 13 is in contact with the p.sup.+-type collector region 11. Also, the collector electrode 13, doubling as a cathode electrode, is in contact with the n.sup.+-type cathode region 12.
(57) Next, a description will be given of the anode ratio . The anode ratio can be expressed as the proportion of the area of the p-type anode region 5-2 exposed on the substrate front surface in one unit region disposed in a mesa portion between neighboring trenches 2 with respect to the area of the unit region exposed on the substrate front surface (surface area). Specifically, the anode ratio is expressed by Expression (1) below. The anode ratio is set based on a width (not including an increase caused by thermal diffusion) Lp in the trench 2 longitudinal direction of the p-type anode region 5-2, taking deviation in the alignment of an ion implantation mask for forming the p-type anode region 5-2, and the like, into consideration.
=Lp/Lc=Lp/(Lp+Ln)(1)
(58) Specifically, the anode ratio is taken to be, for example, 50% to 75%. That is, the p-type anode region 5-2 is disposed thinned out so that the area of the p-type anode region 5-2 exposed before thermal diffusion is equal to or greater than the area of the n.sup.-type drift region 1 exposed on the substrate front surface in one unit region disposed in a mesa portion between neighboring trenches 2 in the FWD portion 22. Preferably, it is good when the anode ratio is near 75%. Thinning out the p-type anode region 5-2 means providing a region in which the p-type anode region 5-2 is not disposed, thereby causing the n.sup.-type drift region 1 and p-type anode region 5-2 to be exposed alternately in the trench 2 longitudinal direction.
(59) The width (not including an increase caused by thermal diffusion) Lp in the trench 2 longitudinal direction of the p-type anode region 5-2 is the width in the trench 2 longitudinal direction of an aperture portion (an aperture portion that exposes the formation region of the p-type anode region 5-2) of an ion implantation mask for forming the p-type anode region 5-2. That is, the width (not including an increase caused by thermal diffusion) Lp in the trench 2 longitudinal direction of the p-type anode region 5-2, not including an increase in the width in the trench 2 longitudinal direction of the p-type anode region 5-2 diffused by thermal diffusion processing after an ion implantation, is less than the width w10 in the trench 2 longitudinal direction of the p-type anode region 5-2 after thermal diffusion.
(60) Ln is the width in the trench 2 longitudinal direction of a portion of the n.sup.-type drift region 1 sandwiched by the p-type anode region 5-2 (that is, a second pitch in the trench 2 longitudinal direction of the p-type anode region 5-2). Lc is the sum of the width (not including an increase caused by thermal diffusion) Lp in the trench 2 longitudinal direction of the p-type anode region 5-2 and the width Ln in the trench 2 longitudinal direction of a portion of the n.sup.-type drift region 1 sandwiched by the p-type anode region 5-2 (hereafter referred to as unit length). Although Lp, Ln, and Lc are the widths in the trench 2 longitudinal direction of each region before thermal diffusion, reference signs Lp, Ln, and Lc are each shown in
(61) Next, the results of verifying the relationship between the anode ratio and reverse recovery characteristics are shown in
(62) Specifically, the repetitive pitch of the trench 2 is taken to be 5 m. The width in the lateral direction of the trench 2 is 1 m, and the mesa width w20 between trenches 2 is 4 m. The width (not including an increase caused by thermal diffusion) Lp in the trench 2 longitudinal direction of the p-type anode region 5-2 is taken to be 5 m. Further, by taking the unit length Lc to be 40 m (=12.5%), 20 m (=25%), 10 m (=50%), approximately 6.7 m (=75%), and 5 m (=100%), the anode ratio is changed, and the reverse recovery current Iak calculated. The anode ratio being 100% is a case wherein the p-type anode region 5-2 is not thinned out, that is, a case wherein the p-type anode region 5-2 is exposed over the whole of the substrate front surface in a mesa portion between neighboring trenches 2 in the FWD portion 22 (the same applies to
(63) From the results shown in
(64) Generally, when conductive, excess carriers accumulate to or above the doping concentration of the p-type anode region 5-2 in a portion wherein the surface of the n.sup.-type drift region 1 is in contact with an oxide film (the interlayer dielectric 8) directly rather than across the p-type anode region 5-2. Therefore, the reverse recovery peak current Irp increases in comparison with when the p-type anode region 5-2 is formed over the whole surface, that is, when the anode ratio is 100%. As opposed to this, the invention is such that, rather than an increase when the anode ratio is 50% or more and less than 100%, there is a decrease in comparison with when the anode ratio is 100%. This is a peculiar advantage not seen in existing diodes.
(65) The following can be considered to be a reason for this. When the anode ratio is 50% or more and less than 100%, the interval between neighboring p-type anode regions 5-2 in the trench 2 longitudinal direction is smaller than the width of a pn-junction built-in depletion layer. Therefore, built-in depletion layers spreading from each of neighboring p-type anode regions 5-2 are linked with each other in the n.sup.-type drift region 1 sandwiched by the built-in depletion layers. As the built-in depletion layer has reverse bias with respect to the pn-junction, holes are not implanted into the n.sup.-type drift region 1 to such an extent that the built-in depletion layer is extinguished, even when reverse bias is applied to the pn-junction. That is, the implantation of holes is restricted by the commonly known JFET effect. Therefore, hole implantation efficiency when the anode ratio is 50% or more and less than 100% decreases in comparison with when the anode ratio is 100%. Therefore, the carrier concentration distribution in a state wherein a rated current is flowing is such that there is a relative drop on the p-type anode region 5-2 side compared with the n.sup.+-type cathode region 12 side. The heretofore described series of actions achieves the advantage of reducing the reverse recovery peak current Irp, as shown in
(66) The reason for the reverse recovery peak current Irp increasing when the anode ratio is less than 50% is that, as the built-in depletion layers spreading into the n.sup.-type drift region 1 from the p-type anode region 5-2 on either side are not linked, the JFET effect decreases. Due to the JFET effect decreasing, accumulated carriers directly below the oxide film begin to increase, because of which the reverse recovery peak current Irp increases.
(67) According to the above, it is preferable that the interval between neighboring p-type anode regions 5-2 is of, or less than, a distance such that the built-in depletion layers spreading from each p-type anode region 5-2 link with each other. In this case, the following kind of advantage is further achieved. For example, the width Lp in the trench 2 longitudinal direction of the p-type anode region 5-2 is set to be sufficiently smaller than the mesa width w20 between trenches 2. Therefore, even when the width Lp in the trench 2 longitudinal direction of the p-type anode region 5-2 is small, the interval between neighboring p-type anode regions 5-2 can be of, or less than, a distance such that the built-in depletion layers spreading from each p-type anode region 5-2 link with each other. Therefore, the reverse recovery peak current Irp is further reduced, and the minimum value of the reverse recovery peak current Irp shown in, for example,
(68) Next, a description will be given of a method of manufacturing the semiconductor device according to Embodiment 1, with a case of fabricating (manufacturing) an RC-IGBT of rated voltage 1,200V, rated current 400 A as an example.
(69) When the rated voltage is 1,200V, the resistivity of the silicon substrate is in the region of, for example, 40 cm to 80 cm. Therefore, the resistivity of the n.sup.-type semiconductor substrate 31 may be in the region of, for example, 55 cm. The orientation of the main surface of the silicon substrate is, for example, (100). Next, a p-type guard ring, for example, configuring a voltage withstanding structure is formed on the front surface side of the n.sup.-type semiconductor substrate 31 in an edge termination structure portion omitted from the drawings. The edge termination structure portion is a region that relaxes an electrical field exerted on the n.sup.-type drift region 1 in an active region, thereby maintaining breakdown voltage. The active region is a region in which an RC-IGBT element structure is formed. In the same way, the edge termination structure portion is also omitted from
(70) Specifically, a resist mask (not shown) in which is opened the formation region of the p-type guard ring is formed on the front surface of the n.sup.-type semiconductor substrate 31. Next, with the resist mask as a mask, a p-type impurity such as, for example, boron (B) is ion implanted into the front surface of the n.sup.-type semiconductor substrate 31. Next, after the resist mask is removed, the p-type impurity implanted into the n.sup.-type semiconductor substrate 31 is caused to diffuse by a thermal diffusion processing, whereby the p-type guard ring is formed. Also, as shown in
(71) Next, a portion of the oxide film 32 corresponding to the formation region of the trench 2 is removed by photolithography. Next, with the oxide film 32 as a mask, anisotropic dry etching, for example, is carried out, thereby forming the trench 2 to a predetermined depth in the front surface of the n.sup.-type semiconductor substrate 31. Next, a sacrificial oxide film (not shown) is formed on the inner wall of the trench 2 by sacrificial oxidation, and by the sacrificial oxide film being removed, a defect layer created on the n.sup.-type semiconductor substrate 31 surface by the formation of the trench 2 is removed. Next, the oxide film 32 covering the front surface of the n.sup.-type semiconductor substrate 31 in the active region is removed.
(72) Next, as shown in
(73) Next, as shown in
(74) Next, with the resist mask 35 as a mask, a first ion implantation 41 of a p-type impurity such as, for example, boron is carried out through the screen oxide film 34 into the front surface of the n.sup.-type semiconductor substrate 31. P-type impurity regions 5-1a and 5-2a are formed by the first ion implantation 41 in the n.sup.-type drift region 1 exposed in the first and second aperture portions 35a and 35b of the resist mask 35. Subsequently, the resist mask 35 is removed. At this time, when the p-type base region 5-1 of the IGBT portion 21 and p-type anode region 5-2 of the FWD portion 22 are to be formed to have differing impurity concentrations, it is sufficient to form a further resist mask and carry out a further p-type impurity ion implantation.
(75) Specifically, when the p-type base region 5-1 and p-type anode region 5-2 are to be formed to have differing impurity concentrations, for example, a resist mask in which only the formation region of the p-type base region 5-1 in the region of the IGBT portion 21 is selectively opened is formed first. Next, with this resist mask as a mask, an ion implantation of, for example, boron is carried out at a dose of in the region of 210.sup.13/cm.sup.2 and an acceleration energy of in the region of 100 keV, after which the resist mask is removed. Next, a resist mask in which only the formation region of the p-type anode region 5-2 in the region of the FWD portion 22 is selectively opened is formed. Then, it is sufficient that, with this resist mask as a mask, an ion implantation of, for example, boron is carried out at a dose within a range of in the region of 110.sup.12/cm.sup.2 or more, 110.sup.13/cm.sup.2 or less, and at an acceleration energy of in the region of 100 keV, after which the resist mask is removed.
(76) Next, as shown in
(77) Next, as shown in
(78) Next, as shown in
(79) Next, the interlayer dielectric 8, of BPSG (borophosphosilicate glass) or the like, is formed over the whole of the front surface of the n.sup.-type semiconductor substrate 31. Next, the interlayer dielectric 8 is selectively removed by photolithography, thereby forming the first and second contact holes 8-1 and 8-2. Next, after the emitter electrode 9 is formed on the front surface of the n.sup.-type semiconductor substrate 31 using a general method, the front surface of the n.sup.-type semiconductor substrate 31 is protected with, for example, a resist film (not shown). Next, after the back surface of the n.sup.-type semiconductor substrate 31 is ground, thereby reducing the thickness of the n.sup.-type semiconductor substrate 31 to, for example, 125 m, a grinding strain layer is removed by etching.
(80) Next, a fourth ion implantation of an n-type impurity such as, for example, selenium (Se) is carried out from the back surface of the n.sup.-type semiconductor substrate 31. The fourth ion implantation is an ion implantation for forming the n-type buffer layer 10, and may be carried out at, for example, a dose of in the region of 310.sup.14/cm.sup.2 and an acceleration energy of in the region of 100 keV. A fifth ion implantation of a p-type impurity such as, for example, boron is carried out from the back surface of the n.sup.-type semiconductor substrate 31 into a region shallower than the fourth ion implantation. The fifth ion implantation is an ion implantation for forming the p.sup.+-type collector region 11, and may be carried out at, for example, a dose of in the region of 810.sup.13/cm.sup.2 and an acceleration energy of in the region of 40 keV.
(81) Next, a resist mask (not shown) of a thickness in the region of, for example, 2 m and having an aperture portion that exposes the formation region of the n.sup.+-type cathode region 12, that is, the FWD portion 22, is formed by photolithography on the back surface of the n.sup.-type semiconductor substrate 31. Next, with the resist mask as a mask, a sixth ion implantation of an n-type impurity such as, for example, phosphorus (P) is carried out into the back surface of the n.sup.-type semiconductor substrate 31. The sixth ion implantation may be carried out at, for example, a dose of in the region of 210.sup.15/cm.sup.2 and an acceleration energy of in the region of 110 keV.
(82) Next, the resist mask protecting the front surface of the n.sup.-type semiconductor substrate 31 and the resist mask on the back surface of the n.sup.-type semiconductor substrate 31 are removed. Next, the impurity regions formed by the fourth to sixth ion implantations are activated by carrying out a thermal processing for in the region of 30 minutes at a temperature in the region of, for example, 950 C. Next, an aluminum-silicon (AlSi, for example, Al including 1% Si) film of a thickness in the region of, for example, 5 m is formed on the front surface side of the n.sup.-type semiconductor substrate 31. Then, the emitter electrode 9 is formed by patterning the AlSi film.
(83) Next, an irradiation with, for example, helium (4He) is carried out from the back surface of the n.sup.-type semiconductor substrate 31 at an acceleration energy of in the region of 23 MeV and a dose of in the region of 110.sup.13/cm.sup.2. Next, an annealing (thermal processing) is carried out for in the region of one hour at a temperature in the region of 370 C., thereby causing recovery of defects occurring inside the n.sup.-type semiconductor substrate 31 due to the helium irradiation. Subsequently, the collector electrode 13 is formed by an Al film, Ti film, Ni film, and gold (Au) film being deposited sequentially to thicknesses of in the region of 1 m, 0.07 m, 1 m, and 0.3 m respectively on the back surface of the n.sup.-type semiconductor substrate 31, thereby completing the RC-IGBT shown in
(84) As heretofore described, according to Embodiment 1, reverse recovery current can be reduced, and reverse recovery loss can thereby be reduced, by adopting an anode ratio of 50% to 75%, because of which the diode characteristics can be improved. Also, according to Embodiment 1, no Schottky junction of the emitter electrode and n.sup.-type drift region is formed in the FWD portion, because of which leakage current can be prevented from increasing when in an off-state. Also, according to Embodiment 1, the region in which only the IGBT is provided (the IGBT portion) can be secured over a greater area than in PTL 2 by the IGBT portion and FWD portion being disposed separately. Therefore, even when carriers are extracted from the FWD portion, the carrier concentration in the IGBT portion can be maintained at a high level. Therefore, the on-state resistance can be reduced, and the on-state voltage can thereby be reduced.
(85) (Embodiment 2)
(86) Next, a description will be given of the configuration of a semiconductor device according to Embodiment 2.
(87) That is, a Schottky junction of the n.sup.-type drift region 1 and emitter electrode 9 is formed in the FWD portion 22. It is preferable that a material such as, for example, Al including 1% Si, platinum (Pt), or platinum silicide (PtSi), wherein a height .sub.B of a Schottky barrier at an interface with a silicon portion is 0.8 eV or more, is used as the material configuring at least the portion of the emitter electrode 9 in contact with the silicon portion of the FWD portion 22. By so doing, leakage current can be reduced. This is effective when providing a barrier metal between the emitter electrode 9 and the silicon portion in the IGBT portion 21 for size reduction or the like.
(88) The second difference is that the lower the anode ratio the better (0%), and it is good when the anode ratio is, for example, less than 50%, preferably 25% or less. The reason for this is that the lower the anode ratio , the farther the recovery peak current Irp can be reduced. The results of verifying the relationship between the anode ratio and reverse recovery characteristics are shown in
(89) Using simulation technology, the reverse recovery current Iak is calculated in cases wherein the anode ratio of the semiconductor device according to Embodiment 2 is 15%, 25%, 50%, 75%, and 100%. Specifically, the width (not including an increase caused by thermal diffusion) Lp in the trench 2 longitudinal direction of the p-type anode region 5-2 is taken to be 5 m. Further, by taking the unit length Lc to be approximately 33 m (=15%), 20 m (=25%), 10 m (=50%), approximately 6.7 m (=75%), and 5 m (=100%), the anode ratio is changed, and the reverse recovery current Iak calculated.
(90) From the results shown in
(91) Regarding a method of manufacturing the semiconductor device according to Embodiment 2, it is sufficient that disposition of the p-type anode region 5-2 so that the anode ratio decreases, and formation of the second contact hole 58-2 so that practically the whole of a mesa portion between neighboring trenches 2 in the FWD portion 22 is exposed, are incorporated in the method of manufacturing the semiconductor device according to Embodiment 1. Apart from these two points, the method of manufacturing the semiconductor device according to Embodiment 2 is the same as the method of manufacturing the semiconductor device according to Embodiment 1.
(92) Next, a description will be given of preferable widths of the IGBT portion 21 and FWD portion 22.
(93) A width W.sub.IGBT of the IGBT portion 21 is taken to be the length between neighboring FWD portions 22 in the direction in which the IGBT portion 21 and FWD portion 22 are repeatedly, alternately disposed. That is, the shorter width of the IGBT portion 21, which has, for example, an approximately rectangular planar form, is taken to be W.sub.IGBT. In the same way, a width W.sub.FWD of the FWD portion 22 is taken to be the length between neighboring IGBT portions 21 in the direction in which the IGBT portion 21 and FWD portion 22 are repeatedly, alternately disposed. That is, the shorter width of the FWD portion 22, which has, for example, an approximately rectangular planar form, is taken to be W.sub.FWD. Regarding the width W.sub.IGBT of the IGBT portion 21 and width W.sub.FWD of the FWD portion 22,
(94) As shown in
(95) Specifically, although also depending on the unit cell dimension of the IGBT portion 21, that is the repetitive pitch of the trench 2, when the repetitive pitch of the trench 2 is 1 m or greater, it is necessary that the width W.sub.FWD of the FWD portion 22 is at least 1 m, because of which it is good when the width W.sub.IGBT of the IGBT portion 21 is 20 m or greater. Note that the FWD portion 22 normally bears a greater current density than the IGBT portion 21, with the current density ratio being such that the current density of the FWD portion 22 is two times or more greater than that of the IGBT portion 21. Therefore, the ratio between the widths of the IGBT portion 21 and FWD portion 22 (=W.sub.IGBT/W.sub.FWD) is 2 or more. In this case, taking the width W.sub.FWD of the FWD portion 22 to be 10 m, increase in the on-state voltage can be restricted provided that the width W.sub.IGBT of the IGBT portion 21 is 20 m or greater. Also, it is necessary that when the width W.sub.FWD of the FWD portion 22 is, for example, 100 m, the width W.sub.IGBT of the IGBT portion 21 is 100 m or greater, and when the width W.sub.FWD of the FWD portion 22 is, for example, 1,000 m, the width W.sub.IGBT of the IGBT portion 21 is 1,000 m or greater. When the region width of each of the IGBT portion 21 and FWD portion 22 is greater than the hole diffusion length, current flows in each of the IGBT portion 21 and FWD portion 22, because of which bias occurs in the current. Consequently, it is particularly preferable that the width W.sub.IGBT of the IGBT portion 21 is 300 m or less, in which case it is preferable that the width W.sub.FWD of the FWD portion 22, although also depending on the current density ratio, is 150 m or less. According to the above, it is preferable that the width W.sub.IGBT of the IGBT portion 21 is 20 m or more, 300 m or less, and that the width W.sub.FWD of the FWD portion 22 is 10 m or more, 150 m or less. In particular, by the width W.sub.IGBT of the IGBT portion 21 being 20 m or more, 100 m or less, and the width W.sub.FWD of the FWD portion 22 being 10 m or more, 50 m or less, a balance can be achieved between restricting the snapback phenomenon and the advantage of in-chip current dispersion.
(96) Also, as a Modification Example 1 of Embodiment 2, the mesa width w20 between trenches 2 may be further reduced beyond 4 m. A built-in depletion layer is spreading in the mesa portion from the boundary between the trench 2 and mesa portion. By further reducing the mesa width w20 of the mesa portion, thereby linking the built-in depletion layers spreading from the trench 2 on either side, the mesa portion can be completely depleted at zero bias. Therefore, even when adopting only a Schottky contact of the n.sup.-type drift region 1 and anode electrode, without forming the p-type anode region 5-2, in the FWD portion 22, a depletion layer spreads in the mesa portion from the trench 2, and can cause pinch-off to occur. Therefore, the commonly known barrier height lowering phenomenon with reverse bias of an extent near to the breakdown voltage of the element can be suppressed. Therefore, even when there is no p-type anode region 5-2 such as, for example, an existing MPS (merged PiN Schottky) diode, an increase in leakage current accompanying an increase in reverse bias can be suppressed. Furthermore, as there is absolutely no hole implantation from the p-type anode region 5-2, and the amount of hole implantation is determined by only the barrier height of the barrier metal, hole implantation efficiency can be dramatically reduced.
(97) Actually, not only a Schottky contact of the n.sup.-type drift region 1 and anode electrode, but also the p-type anode region 5-2, of which the trench 2 lateral direction width is further reduced with respect to the mesa width w20 between trenches 2, is formed in the mesa portion, and the repetitive pitch in the trench 2 longitudinal direction of the p-type anode region 5-2 may be ten times or more greater than the mesa width w20 between trenches 2. By so doing, the anode ratio is less than 10%, and hole implantation from the p-type anode region 5-2 can be sufficiently reduced to the extent of being only that of the Schottky contact of the n.sup.-type drift region 1 and anode electrode (anode ratio =0%). Therefore, the reverse recovery peak current Irp can be dramatically reduced, and the p-type anode region 5-2 increases the pinch-off effect of the depletion layer when there is reverse bias. Therefore, leakage current is less liable to be affected by defects at the Schottky interface than when there is only a Schottky contact of the n.sup.-type drift region 1 and anode electrode, and the element characteristics can be stabilized.
(98) Also, as a Modification Example 2 of Embodiment 2, the trench 2 of the FWD portion 22 may be provided at differing trench intervals.
(99) Also, the relationship between the trench interval ratio Lb/La and a forward voltage drop Vf, and the relationship between the trench interval ratio Lb/La and the reverse recovery peak current Irp, when the second trench interval Lb of the trench 2 is greater than the first trench interval La are shown in
(100) The reason for the advantage of the decrease in the reverse recovery current I.sub.AK being large in comparison with the forward voltage drop Vf when the trench interval ratio Lb/La is greater than 1 will be described using
(101) When the trench interval ratio Lb/La=8, the sum (hereafter, the pitch La+Lb) of the smallest numerals (that is, 1 and 8) among positive integers satisfying the trench interval ratio Lb/La=8 is 9 (=1+8), and when the trench interval ratio Lb/La=1, the pitch La+Lb is 2 (=1+1). That is, the pitch La+Lb when the trench interval ratio Lb/La=8 is 4.5 times greater than the pitch La+Lb when the trench interval ratio Lb/La=1, and the current density when the trench interval ratio Lb/La=8 is lower overall by that amount than the current density when the trench interval ratio Lb/La=1. Furthermore, when the trench interval ratio Lb/La=8, the current density of the narrow region of the semiconductor substrate 81 sandwiched by trenches 82 neighboring at the first trench interval La is higher than the current density of another region. In particular, the pitch La+Lb being large is the reason the increase in the forward voltage drop of is suppressed to in the region of 2%. Meanwhile, in the case of the reverse recovery current I.sub.AK, operation in the narrow region of the semiconductor substrate 81 sandwiched by trenches 82 neighboring at the first trench interval La becomes a main operation by the anode region (not shown) being partitioned (divided) into multiple portions by the trench 82, because of which the implantation efficiency decreases. Therefore, discharge of holes when there is a reverse recovery operation is facilitated, and the reverse recovery peak current Irp decreases.
(102) According to the above, it is good when the trench interval ratio Lb/La is greater than 1 (1<Lb/La), and preferably 2 or greater (2Lb/La). Also, as the characteristics are practically saturated when the trench interval ratio Lb/La is 10 or greater, it is good when the trench interval ratio Lb/La is 10 or less (Lb/La10), and preferably, it is good when the trench interval ratio Lb/La is 5 or less (Lb/La5), which can reduce the forward voltage. When focusing only on the reverse recovery current I.sub.AK, the trench interval ratio Lb/La may be 10 or greater, but as current is liable to concentrate in a narrow region sandwiched by trenches 82 neighboring at the first trench interval La, it is preferable in terms of preventing current concentration too that the trench interval ratio Lb/La is 10 or less.
(103) In the case of Modification Example 2 of Embodiment 2, the same advantages are achieved even when the anode ratio is 100%, that is, the p-type anode region is formed over the whole of the FWD portion 22.
(104) As heretofore described, according to Embodiment 2, the same advantages as in Embodiment 1 can be obtained. Also, according to Embodiment 2, the reverse recovery peak current can be further reduced by a Schottky junction of the n.sup.-type drift region and emitter electrode being formed in the FWD portion. Also, according to Embodiment 2, by the p-type anode region being disposed thinned out, a depletion layer extending from the pn-junction between the p-type anode region and n.sup.-type drift region, and from the boundary between the trench and n.sup.-type drift region, is easily pinched off, because of which leakage current can be prevented from increasing when in an off-state.
(105) (Embodiment 3)
(106) Next, a description will be given of the configuration of a semiconductor device according to Embodiment 3.
(107) As heretofore described, according to Embodiment 3, the same advantages as in Embodiments 1 and 2 can be obtained.
(108) (Embodiment 4)
(109) Next, a description will be given of the configuration of a semiconductor device according to Embodiment 4.
(110) For example, when the rated voltage is 600V to 6,500V, the resistivity of an n.sup.-type silicon substrate that is to form the n.sup.-type drift region 1 is typically 30 cm to 325 cm, wherein the unit of a value that is 0.05 times the rated voltage is converted. Therefore, the width of a built-in depletion layer spreading in the mesa portion from the trench 2 on one side, using Poisson's equation, is approximately 2.4 m to 7.8 m. Consequently, provided that the mesa width w20 between trenches 2 is less than 4.8 m to 15.6 m when the rated voltage is 600V to 6,500V, the built-in depletion layers spreading from the trench 2 on either side of the mesa portion link up. More preferably, by further reducing the mesa width w20 between trenches 2 so as to be, for example, 2.4 m to 7.8 m or less, half of the previously mentioned values, when the rated voltage is 600V to 6,500V, an increase in leakage current due to the mirror image effect can be still more reliably suppressed.
(111) When the mesa width w20 between trenches 2 is 4.8 m to 15.6 m when the rated voltage is 600V to 6,500V, taking the rated voltage to be V and the trench mesa width to be W, it is sufficient that the mesa width w20 with respect to the rated voltage V is calculated in accordance with Expression (2) below.
W=1.1259010.sup.21.Math.v.sup.6+2.3608110.sup.17.Math.v.sup.52.0094710.sup.13.Math.v.sup.4+9.1589910.sup.10.Math.v.sup.32.5580810.sup.6.Math.v.sup.2+6.1140310.sup.3.Math.V+2.0100510.sup.0(2)
(112) Expression (2) defines the resistivity of a typical semiconductor substrate with respect to the rated voltage V using the heretofore described method, and is such that the built-in depletion layer width is obtained in accordance with Poisson's equation at seven points of the rated voltage V between 600V and 6,500V (600V, 1,200V, 1,700V, 2,500V, 3,300V, 4,500V, and 6,500V), and the values fitted with a sextic polynomial expression. When reducing the mesa width w20 between trenches 2, it is sufficient that the mesa width w20 is smaller than the value of the mesa width w20 calculated using Expression (2), for example, it is sufficient that the mesa width w20 between trenches 2 is one-half of the value of the mesa width w20 calculated using Expression (2).
(113) Also, as shown in
(114) In this way, according to Embodiment 4, a diode wherein increase in leakage current is suppressed can be obtained by sufficiently reducing the mesa width between trenches, even when there is no p-type anode region.
(115) (Embodiment 5)
(116) Next, a description will be given of the configuration of a semiconductor device according to Embodiment 5.
(117)
(118) Also, by the depletion layer end 91 of the built-in depletion layer 90 being of a form near that of a planar junction, a decrease in the barrier height at a Schottky contact can also be restricted, because of which there is almost no increase in leakage current even when a high voltage is applied. Furthermore, even when the second pitch in the trench 2 longitudinal direction of the p-type anode region 5-2 is sufficiently longer than the width of the built-in depletion layer 90, and the anode ratio is 10% or less, neither breakdown voltage nor leakage current depends on the second pitch in the trench 2 longitudinal direction of the p-type anode region 5-2. Therefore, implantation of holes from the p-type anode region 5-2 into the n.sup.-type drift region 1 can be practically ignored. Also, as shown in
(119) As heretofore described, according to Embodiment 5, the same advantages as in Embodiments 3 and 4 can be obtained.
(120) (Embodiment 6)
(121) Next, a description will be given of the configuration of a semiconductor device according to Embodiment 6.
(122) In Embodiment 6 too, in the same way as in Embodiment 5, the surface form of the depletion layer end 91 of the built-in depletion layer 90 is sufficiently near that of a planar junction, even when there is no p-type anode region 5-2, owing to the repetitive pitch of the trench 2 being sufficiently small. Further, by not forming the p-type anode region 5-2, the hole implantation efficiency from the p-type anode region 5-2 into the n.sup.-type drift region 1 can be reduced to practically 0 (zero) without causing a decrease in breakdown voltage or an increase in leakage current. When forming the anode electrode 59 using an aluminum-silicon (AlSi) alloy, platinum silicide (PtSi), or the like, which have a high Schottky barrier, hole implantation from the p-type anode region 5-2 into the n.sup.-type drift region 1 occurs, because of which the hole implantation efficiency cannot be reduced to zero, but the hole implantation efficiency can be reduced to one-half or less compared with that when forming the p-type anode region 5-2.
(123) Also, as shown in
(124) The diode structures described in Embodiments 4 to 6 may also be applied to the FWD portion 22 of the semiconductor device in Embodiment 2. Also, the shallow p-type layer 5-3 in the modification example of Embodiment 6 may be formed in Embodiments 4 and 5. By so doing, the same advantages as in Embodiment 6 can be achieved.
(125) As heretofore described, according to Embodiment 6, the same advantages as in Embodiments 3 to 5 can be obtained.
(126) (Embodiment 7)
(127) Next, a description will be given of the configuration of a semiconductor device according to Embodiment 7.
(128) Specifically, as shown in
(129) The contact electrode 18 is embedded inside each of, for example, the first and second contact holes 8-1 and 8-2. The contact electrode 18 realizes good ohmic contact, even when an aperture width w31 in the trench 2 lateral direction of the first contact hole 8-1 and the aperture width w21 in the trench 2 lateral direction of the second contact hole 8-2 are small due to a repetitive pitch L30 of the trench 2 being small at, for example, 4 m or less. For example, when the contact electrode 18 is not included, as in the comparison example shown in
(130) Meanwhile, the invention is such that the interiors of the first and second contact holes 8-1 and 8-2 can be completely filled by the contact electrode 18 formed of the titanium layer 14, titanium nitride layer 15, and tungsten layer 16. Therefore, the gap 19 can be prevented from occurring between the emitter electrode 9 and silicon portion. Specifically, the titanium layer 14 is provided along the side walls and substrate front surface inside each of the first and second contact holes 8-1 and 8-2. The titanium layer 14 is in contact with the n.sup.+-type emitter region 6 and p.sup.+-type contact region 7 in the IGBT portion 21, and in contact with the p-type anode region 5-2 and p.sup.+-type contact region 17 in the FWD portion 22. The titanium nitride layer 15 is provided along the titanium layer 14, on the inner side of the titanium layer 14, inside the first and second contact holes 8-1 and 8-2, and the tungsten layer 16 is provided on the inner side of the titanium nitride layer 15. The emitter electrode 9 is in contact with the titanium layer 14, titanium nitride layer 15, and tungsten layer 16.
(131) Also, for example, when the gate electrode 4 in the FWD portion 22 is of the gate potential, it has been confirmed by the inventors that, when attempting a reduction in on-state voltage in the IGBT portion by reducing the repetitive pitch L30 of the trench 2 to, for example, 4 m or less, the forward voltage when gate voltage is applied rises considerably. For example, when applying a commonly used gate voltage of 15V, the rate of rise of the forward voltage, compared to when no gate voltage is applied (=0V), is in the region of 3% when the repetitive pitch L30 of the trench 2 is 5 m, in the region of 10% when the repetitive pitch L30 of the trench 2 is 4 m, and in the region of 21% when the repetitive pitch L30 of the trench 2 is 2.3 m. Also, the rate of rise of the forward voltage increases in proportion to the size of the gate voltage. The reason for this is as follows. When gate voltage is applied, electrons concentrate in the periphery of the trench 2, because of which hole implantation from the p-type anode region 5-2 into the n.sup.-type drift region 1 is restricted by the electrons concentrated in the periphery of the trench 2 in the FWD portion 22. The more the repetitive pitch L30 of the trench 2 is reduced, the smaller the width in the trench 2 lateral direction (the portion indicated by reference sign w20 in
(132) Therefore, applying Embodiment 3 to Embodiment 7, the gate electrode 4 in the FWD portion 22 and the emitter electrode 9 may be conductively connected. Owing to the gate electrode 4 in the FWD portion 22 and the emitter electrode 9 being conductively connected, electrons do not concentrate in the periphery of the trench 2 in the FWD portion 22 when gate voltage is applied. Therefore, even when the repetitive pitch L30 of the trench 2 is miniaturized, hole implantation from the p-type anode region 5-2 into the n.sup.-type drift region 1 is not restricted by electrons, because of which the forward voltage can be reduced. Also, as shown in
(133) As heretofore described, according to Embodiment 7, the same advantages as in Embodiments 1 and 2 can be obtained. According to Embodiment 7, even when attempting a reduction in on-state voltage by reducing the repetitive pitch of the trench to, for example, 4 m or less, a rise in the forward voltage when gate voltage is applied can be restricted, and good ohmic contact can be realized on the anode side of the FWD portion.
(134) The invention not being limited by the heretofore described embodiments, various changes are possible without departing from the scope of the invention. For example, the dimensions, surface concentrations, and the like of each portion in each of the heretofore described embodiments are variously set in accordance with the required specifications or the like. Also, in each embodiment, a first conductivity type is taken to be n-type and a second conductivity type is taken to be p-type, but the invention is established in the same way when the first conductivity type is p-type and the second conductivity type is n-type.
INDUSTRIAL APPLICABILITY
(135) As heretofore described, the semiconductor device according to the invention is useful in a power semiconductor device used in a power conversion device or the like.
REFERENCE SIGNS LIST
(136) 1 n.sup.-type drift region
(137) 2 Trench
(138) 3 Gate insulating film
(139) 4, 54 Gate electrode
(140) 5-1 p-type base region
(141) 5-2 p-type anode region
(142) 6 n.sup.+-type emitter region
(143) 6-1 n.sup.+-type emitter region configuration portion (first n.sup.+-type region)
(144) 6-2 n.sup.+-type emitter region configuration portion (second n.sup.+-type region)
(145) 7 p.sup.+-type contact region
(146) 8 interlayer dielectric
(147) 8-1 IGBT portion contact hole (first contact hole)
(148) 8-2 FWD portion contact hole (second contact hole)
(149) 9 Emitter electrode
(150) 10 n-type buffer layer
(151) 11 p.sup.+-type collector region
(152) 12 n.sup.+-type cathode region
(153) 13 Collector electrode
(154) 21 IGBT portion
(155) 22 FWD portion
(156) Lc Unit length
(157) Lp Width in trench longitudinal direction of p-type anode region (not including an increase caused by thermal diffusion)
(158) Ln Width in trench longitudinal direction of portion of n.sup.-type drift region sandwiched by p-type anode region (not including an increase caused by thermal diffusion)
(159) w10 Width in trench longitudinal direction of p-type anode region
(160) w20 Width in trench lateral direction of p-type anode region (mesa width)
(161) w11 Aperture width in trench longitudinal direction of second contact hole
(162) w21 Aperture width in trench lateral direction of second contact hole
(163) x11 Width in trench longitudinal direction of p-type base region
(164) x12 Width in trench longitudinal direction of portion of n.sup.-type drift region sandwiched by p-type base region
(165) Anode ratio