OPTICAL MODULATOR
20170336696 · 2017-11-23
Inventors
- Ken Tsuzuki (Atsugi-shi, Kanagawa-ken, JP)
- Shin Kamei (Atsugi-shi, Kanagawa-ken, JP)
- Makoto Jizodo (Atsugi-shi, Kanagawa-ken, JP)
Cpc classification
G02F1/2257
PHYSICS
International classification
Abstract
The present invention provides an optical modulator including a substrate and a phase modulation portion on the substrate. The phase modulation portion includes an optical waveguide comprised of a first clad layer, a semiconductor layer that is laminated on the first clad layer and has a refraction index higher than the first clad layer and a second clad layer that is laminated on the semiconductor layer and has a refraction index lower than the semiconductor layer, a first traveling wave electrode, and a second traveling wave electrode. The semiconductor layer includes a rib that is formed in the optical waveguide in an optical axis direction and is a core of the optical waveguide, a first slab that is formed in the optical axis direction in one side of the rib, a second slab that is formed in the optical axis direction in the other side of the rib, a third slab that is formed in the first slab in the optical axis direction at the opposite side to the rib, and a fourth slab that is formed in the second slab in the optical axis direction at the opposite side to the rib. The first slab is formed to be thinner than the rib and the third slab, and the second slab is formed to be thinner than the rib and the fourth slab.
Claims
1. An optical modulator (300) comprising: a substrate (401); and a phase modulation portion (311) on the substrate, the phase modulation portion (311) including an optical waveguide (323) comprised of a first clad layer (402), a semiconductor layer (403) that is laminated on the first clad layer (402) and has a refraction index higher than the first clad layer (402) and a second clad layer (404) that is laminated on the semiconductor layer (403) and has a refraction index lower than the semiconductor layer (403), a first traveling wave electrode (321), and a second traveling wave electrode (322), wherein the semiconductor layer (403) includes: a rib (C0) that is formed in the optical waveguide (323) in an optical axis direction and is a core of the optical waveguide (323); a first slab (C1) that is formed in the optical axis direction in one side of the rib (C0); a second slab (C2) that is formed in the optical axis direction in the other side of the rib (C0); a third slab (C3) that is formed in the first slab (C1) in the optical axis direction at the opposite side to the rib (C0); and a fourth slab (C4) that is formed in the second slab (C2) in the optical axis direction at the opposite side to the rib (C0), wherein the first slab (C1) is formed to be thinner than the rib (C0) and the third slab (C3), and the second slab (C2) is formed to be thinner than the rib (C0) and the fourth slab (C4).
2. The optical modulator (300) according to claim 1, wherein when a thickness of the rib (C0) is indicated at t0, a thickness of the first slab (C1) is indicated at t1 and a thickness of the third slab (C3) is indicated at t3, a relation of the thicknesses meets an unequal expression of t0>t3>t1, and when a thickness of the second slab (C2) is indicated at t2 and a thickness of the fourth slab (C4) is indicated at t4, a relation of the thicknesses meets an unequal expression of t0>t4>t2.
3. The optical modulator (300) according to claim 2, wherein a relation of the thicknesses further meets an unequal expression of t0/2>t1 and an unequal expression of t0/2>t2.
4. The optical modulator (300) according to claim 3, wherein the first traveling wave electrode (321) is formed in the optical axis direction on an upper surface of an end in the third slab (C3) at the opposite side to the rib (C0), and the second traveling wave electrode (322) is formed in the optical axis direction on an upper surface of an end in the fourth slab (C4) at the opposite side to the rib (C0).
5. The optical modulator (300) according to claim 4, wherein an end of the third slab (C3) at the opposite side to the first slab (C1) is a high-concentration p-type semiconductor region (403-3) and an end of the fourth slab (C4) at the opposite side to the second slab (C2) is a high-concentration n-type semiconductor region (403-4), and the first slab (C1)-side of the third slab (C3), the first slab (C1) and the first slab (C1)-side of the rib (C0) are an intermediate-concentration p-type semiconductor region (403-1), and the second slab (C2)-side of the fourth slab (C4), the second slab (C2) and the second slab (C2)-side of the rib (C0) are an intermediate-concentration n-type semiconductor region (403-2).
6. The optical modulator according to claim 5, wherein a junction portion between the intermediate-concentration p-type semiconductor region (403-1) and the intermediate-concentration n-type semiconductor region (403-2) has a p-n junction structure.
7. The optical modulator (300) according to claim 5, wherein a junction portion between the intermediate-concentration p-type semiconductor region (403-1) and the intermediate-concentration n-type semiconductor region (403-2) has a p-i-n junction structure in which an i-type (intrinsic) semiconductor region not doped is further interposed between the intermediate-concentration p-type semiconductor region (403-1) and the intermediate-concentration n-type semiconductor region (403-2).
8. The optical modulator (300) according to claim 3, wherein when a width of the first slab (C1) is indicated at w1 and a width of the second slab (C2) is indicated at w2, a relation of the w1 meets an unequal expression of 60 nm<w1<600 nm, and a relation of the w2 meets an unequal expression of 60 nm<w2<600 nm.
9. The optical modulator (300) according to claim 2, wherein in a connecting portion between the phase modulation portion (311) and a rib waveguide formed in the optical modulator, a width in a region of each of the first slab (C1) and the second slab (C2) of the phase modulation portion (311) is gradually narrower toward the phase modulator.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0026]
[0027]
[0028]
[0029]
[0030]
[0031]
[0032]
[0033]
[0034]
[0035]
[0036]
[0037]
DESCRIPTION OF EMBODIMENTS
[0038] Hereinafter, an explanation will be made of embodiments of the present invention with reference to the accompanying drawings.
First Embodiment
[0039]
[0040] The phase modulation portion 311 includes traveling wave electrodes 321 and 322 and an optical waveguide 323 that extend in an x axis direction, and by applying a voltage to the traveling wave electrodes 321 and 322, changes a phase of light that wave-guides in the optical waveguide 323. The phase modulation portion 312 includes traveling wave electrodes 324 and 325 and an optical waveguide 326 that extend in the x axis direction, and by applying a voltage to the traveling wave electrodes 324 and 325, changes a phase of light that wave-guides in the optical waveguide 326. The optical waveguides 323 and 326 each have the structure called a rib waveguide including: an Si semiconductor layer that is configured of a rib portion as a core of the optical waveguide formed in the optical axis direction and slab portions that are formed in both sides of the rib portion and are thinner than the rib portion; and SiO.sub.2 clad layers formed upward and downward of the Si semiconductor layer.
[0041]
[0042] The optical waveguide 323 has the structure of a rib waveguide further deformed, and the Si semiconductor layer 403 in which light wave-guides is interposed between the first SiO.sub.2 clad layer 402 and the second SiO.sub.2 clad layer 404. The Si semiconductor layer 403 includes the rib portion C0 in an Si semiconductor layer region thicker in the center as a core. The Si semiconductor layer 403 includes a first slab portion C1 and a second slab portion C2 that are arranged in both sides of the rib portion C0 and are Si semiconductor layer regions thinner than the rib portion C0. Further, the Si semiconductor layer 403 includes a third slab portion C3 that is arranged in an end of the first slab portion C1 at the opposite side to the rib portion C0, and is the Si semiconductor layer region thinner than the rib portion C0 and thicker than the first slab portion C1 adjacent thereto, and a fourth slab portion C4 that is arranged in an end of the second slab portion C2 at the opposite side to the rib portion C0, and is the Si semiconductor layer region thinner than the rib portion C0 and thicker than the second slab portion C2 adjacent thereto.
[0043] That is, it can be said that the semiconductor layer 403 has the structure that the first slab portion C1 is inserted between the rib portion C0 that is the core of the optical waveguide 323 and the third slab portion C3 formed in one side of the rib portion C0, and the second slab portion C2 is inserted between the rib portion C0 and the fourth slab portion C4 formed in the other side of the rib portion C0.
[0044] The optical waveguide 323 confines the light using a difference in a refraction index between the Si semiconductor layer 403, and the first SiO.sub.2 clad layer 402 and the second SiO.sub.2 clad layer 404 in the periphery of the Si semiconductor 403.
[0045] The traveling wave electrode 321 is formed in the x axis direction on an upper surface of an end of the third slab portion C3 in the Si semiconductor layer 403 at the opposite side to the first slab portion C1, and the traveling wave electrode 322 is formed in the x axis direction on an upper surface of an end of the fourth slab portion C4 in the Si semiconductor layer 403 at the opposite side to the second slab portion C2.
[0046] The Si semiconductor layer 403 has conductivity by doping of Si with implantation of ions such as boron (B), phosphorous (P) or arsenic (As). Here, the Si semiconductor layer 403 includes five regions that are different in a doping concentration. The end of the third slab portion C3 in the Si semiconductor layer 403 at the opposite side to the first slab portion C1 becomes a high-concentration p-type semiconductor region 403-3, and the end of the fourth slab portion C4 in the Si semiconductor layer 403 at the opposite side to the second slab portion C2 becomes a high-concentration n-type semiconductor region 403-4. The first slab portion C1-side of the third slab portion C3 in the Si semiconductor layer 403, the first slab portion C1 and the first slab portion C1-side of the rib portion C0 become an intermediate-concentration p-type semiconductor region 403-1. The second slab portion C2-side of the fourth slab portion C4 in the Si semiconductor layer 403, the second slab portion C2 and the second slab portion C2-side of the rib portion C0 become an intermediate-concentration n-type semiconductor region 403-2.
[0047] A boundary of the high-concentration p-type semiconductor region 403-3 makes contact with a boundary of the intermediate-concentration p-type semiconductor region 403-1, and a boundary of the high-concentration n-type semiconductor region 403-4 makes contact with a boundary of the intermediate-concentration n-type semiconductor region 403-2. The boundaries may be subjected to doping in a state of overlapping. The rib portion C0 has a p-n junction structure in which the intermediate-concentration p-type semiconductor region 403-1 makes contact with the intermediate-concentration n-type semiconductor region 403-2. The other example may include a p-i-n junction structure in which an i-type (intrinsic) semiconductor region is interposed between the intermediate-concentration p-type semiconductor region 403-1 and the intermediate-concentration n-type semiconductor region 403-2.
[0048] By applying an inversely-biased electrical field in the p-n junction portion or the p-i-n junction portion of the rib portion C0, a carrier density in the inside of the core (rib portion C0 of the Si semiconductor layer 403) of the optical waveguide 323 changes and a refraction index of the optical waveguide changes (carrier plasma effect), thereby modulating the phase of the light.
[0049] Next, an explanation will be made of a method for determining a dimension of each of the rib portion and the first to fourth slab portions in the cross-section surface of the Si semiconductor layer 403 described in
[0050] First, an explanation will be made of the thickness t0 of the rib portion C0, the thickness t1 of the first slab portion C1, the thickness t2 of the second slab portion C2, the thickness t3 of the third slab portion C3 and the thickness t4 of the fourth slab portion C4. In the optical waveguide 323, the light is confined within the rib portion C0 in the Si semiconductor layer 403 as the core of the optical waveguide 323. Here, when the third slab portion C3 and the fourth slab portion C4, which are Si semiconductor layers having an effective refraction index equivalent to or higher than the rib portion C0, are positioned in close proximity to the rib portion C0, mode coupling is caused and the light transfers to the third slab portion C3 and the fourth slab portion C4 in close proximity to the rib portion C0 in a constant propagation length. Therefore, the light having transferred to the third slab portion C3 and the fourth slab portion C4 in close proximity to the rib portion C0 causes an optical loss of the modulator. The light having transferred to the third slab portion C3 and the fourth slab portion C4 repeats coming and going between the rib portion C0, and the third slab portion C3 and the fourth slab portion C4, causing the loss to vary depending upon a propagating wavelength. Three methods as follows will be conceived for preventing this loss of the light.
[0051] First, a first method is not to position the third slab portion C3 and the fourth slab portion C4 in close proximity to the rib portion C0. A second method is to suppress a length of a section, which is in close proximity to the rib portion C0, of each of the third slab portion C3 and the fourth slab portion C4 to be short. A third method is to make an effective refraction index of each of the third slab portion C3 and the fourth slab portion C4 in close proximity to the rib portion C0 smaller than an effective refraction index of the rib portion C0 in which the light is propagating. Hereinafter, the three methods will be considered.
[0052] The first method for not positioning the third slab portion C3 and the fourth slab portion C4 in close proximity to the rib portion C0 will be considered. For not positioning the third slab portion C3 and the fourth slab portion C4 in close proximity to the rib portion C0, there is a method of making the width w1 of the first slab portion C1 and the width w2 of the second slab portion C2 large, but as the w1 is the larger, a cross-sectional area of the intermediate-concentration p-type semiconductor region 403-1 becomes the smaller, and as the w2 is the larger, a cross-sectional area of the intermediate-concentration n-type semiconductor region 403-2 becomes the smaller and a resistance of Si semiconductor layer 403 becomes the higher. Accordingly, since the first method results in having the structure that is not different from that of the conventional MZ type optical modulator described in
[0053] The second method for suppressing the length of the section, which is in close proximity to the rib portion C0, of each of the third slab portion C3 and the fourth slab portion C4 to be short will be considered. In the Si semiconductor layer 403, for shortening the length of the section, which is in close proximity to the rib portion C0, of each of the third slab portion C3 and the fourth slab portion C4, the length of the section of each of the third slab portion C3 and the fourth slab portion C4 is made short. That is, it is necessary to shorten an entire length of the phase modulation portion 311. It is possible to suppress the mode coupling by shortening the entire length of the phase modulation portion 311. In this case, however, a length of the traveling wave electrode is also required to be short. Then, since the modulation efficiency is determined by VπL, it is necessary to increase the phase inversion voltage Vπ for making the modulation efficiency constant. In this case, the MZ type optical modulator 300 cannot be driven in low consumption power, which is difficult to be adopted in the present embodiment.
[0054] The third method for making the effective refraction index of each of the third slab portion C3 and the fourth slab portion C4 which are in close proximity to the rib portion C0 smaller than the effective refraction index of the rib portion C0 in which the light is propagating will be considered. For making the effective refraction index of each of the third slab portion C3 and the fourth slab portion C4 which are in close proximity to the rib portion C0 smaller than the effective refraction index of the rib portion C0 in which the light is propagating, a thickness of each of the third slab portion C3 and the fourth slab portion C4 which are in close proximity to the rib portion C0 is made thin to cause the light to leak into the first clad layer 402 and the second clad layer 404 in the upward side and the downward side of the Si semiconductor layer 403, making it possible to realize the third method.
[0055] In the present embodiment, a relation of t0, t1 and t3 is made to meet an unequal expression of t0>t3>t1. When the relation of t0, t1 and t3 meets this unequal expression, an effective refraction index of light propagating in the third slab portion C3 can be made smaller than an effective refraction index of the light propagating in the rib portion C0. In addition, a relation of t0, t2 and t4 is made to meet an unequal expression of t0>t4>t2. When the relation of t0, t2 and t4 meets the unequal expression, an effective refraction index of light propagating in the fourth slab portion C4 can be made smaller than an effective refraction index of the light propagating in the rib portion C0. Therefore, even when the rib portion C0 is positioned in close proximity to the third slab portion C3 or the fourth slab portion C4, the optical loss can be suppressed with no transfer of the light to the third slab portion C3 and the fourth slab portion C4. Here, t1 and t2 each may be the same value or a different value, and t3 and t4 each may be the same value or a different value. Further, w1 and w2 each may be the same value or a different value, and w3 and w4 each may be the same value or a different value.
[0056] In addition, also in the present embodiment, as similar to the conventional MZ type optical modulator 100 described in
[0057] Two methods as follows will be conceived for lowering the resistance of each of the resistances R1 and R2. First of all, the first method is to increase a doping concentration of each of the intermediate-concentration p-type semiconductor region 403-1 and the intermediate-concentration n-type semiconductor region 403-2 to increase the carrier density. The second method is to thicken the first slab portion C1 and the second slab portion C2 in both the sides of the rib portion C0.
[0058] First, the first method will be considered. Increasing the doping concentration and the carrier density of the intermediate-concentration p-type semiconductor region 403-1 and the intermediate-concentration n-type semiconductor region 403-2 leads to increasing a doping concentration of the rib portion C0 in the Si semiconductor layer 403 as the core of the optical waveguide 323. In this case, in a doping region of the rib portion C0 in the Si semiconductor layer 403, since optical absorption by the carrier is made large, it is not possible to suppress the optical loss of the optical waveguide 323. Accordingly, the first method is not appropriate in the present embodiment.
[0059] Next, the second method will be considered. In the present embodiment, the third slab portion C3 and the fourth slab portion C4 thicker than the first slab portion C1 and the second slab portion C2 are provided further outside of the first slab portion C1 and the second slab portion C2. Providing the third slab portion C3 and the fourth slab portion C4 causes an increase in a cross-sectional area of each of the intermediate-concentration p-type semiconductor region 403-1 and the intermediate-concentration n-type semiconductor region 403-2. Then, it is possible to lower the resistance value of each of the resistances R1 and R2. At this time, when an optical waveguide in a distance w.sub.pn in a region between the high-concentration p-type semiconductor region 403-3 and the high-concentration n-type semiconductor region 403-4 is made as wide as and as thick as possible, it is possible to obtain the better effect.
[0060] On the other hand, when the thickness of each of the first slab portion C1 and the second slab portion C2 is made closer to the thickness of the rib portion C0, leak of a field of light into the third slab portion C3 and the fourth slab portion C4 is made large, and the field of the light enters the third slab portion C3 and the fourth slab portion C4 to increase the loss of the optical waveguide. Further, the field of the light existing in a region where the refraction index changes is reduced to be small due to the carrier plasma effect, therefore leading to degradation of the modulation efficiency as well. Therefore it is preferable that the thickness t1 of the first slab portion C1 and the thickness t2 of the second slab portion C2 are a half of the rib portion C0 or less, that is, an unequal expression of t0/2>t1 and an unequal expression of t0/2>t2 are met.
[0061] Further, since the high-concentration p-type semiconductor region 403-3 and the high-concentration n-type semiconductor region 403-4 each have a sufficient carrier concentration and are low in resistivity, even when t1 and t2 have the thickness to meet the aforementioned unequal expressions, an increase in the resistance value does not almost influence characteristics of the modulator. Therefore it is preferable to position the boundary between the high-concentration p-type semiconductor region 403-3 and the intermediate-concentration n-type semiconductor region 403-1 and the boundary between the high-concentration p-type semiconductor region 403-3 and the intermediate-concentration n-type semiconductor region 403-2 respectively in a region of the third slab portion C3 of the thickness t3 and in a region of the fourth slab portion C4 of the thickness t4 formed outside of the first slab portion C1 and the second slab portion C2, because the most effect of the invention can be obtained.
[0062] Next, the width w0 of the rib portion C0, the width w1 of the first slab portion C1, the width w2 of the second slab portion C2, the width w3 of the third slab portion C3 and the width w4 of the fourth slab portion C4 will be explained. In the present embodiment, as described before, in a case where the width w1 of the first slab portion C1 and the width w2 of the second slab portion C2 are made as small as possible, it is possible to obtain the more effect. However, since aligning accuracy of a photo mask at the production of the MZ type optical modulator 300 is approximately ±60 nm, if the width of each of w1 and w2 is set to 60 nm or less, it is assumed that w1 and w2 will not be formed due to variations at the production. Then, since the neighbors of the rib portion C0 are the third slab portion C3 and the fourth slab portion C4 having the second thickness to the rib portion C0, the field of the light leaks largely from the rib portion C0 to cause an increase in an optical loss or a reduction in a modulation efficiency. On the other hand, when w1 and w2 are large, the structure is closer to the structure of the conventional MZ type optical modulator 100 illustrated in
TABLE-US-00001 TABLE 1 Electrical field Increase rate Attenuation intensity in electrical constant α (V/m) field intensity (Np/m) MZ type optical 1.64E+07 0 85.5 modulator 100 (FIG. 1: conventional structure) w1 (w2) = 1000 nm 1.66E+07 1.1% 83.8 w1 (w2) = 400 nm 1.91E+07 16.2% 75.1 w1 (w2) = 200 nm 2.06E+07 25.6% 67.1
[0063] The electrical field intensity, as compared to the conventional MZ type optical modulator 100, increases by 25.6% when w1 (w2) is 200 nm, and by 16.2% when w1 (w2) is 400 nm, but by 1.1% only when w1 (w2) is 1000 nm, by which the effect of the invention cannot be nearly obtained. Therefore it is preferable to set the value of w1 to a value to meet the unequal expression of 60 nm<w1 (w2)<600 nm, because it is possible to obtain the maximum effect of the invention.
[0064] Si semiconductor layers having the same thickness with the rib portion C0 as the optical waveguide layer can be formed outside of the third slab portion C3 and the fourth slab portion C4. In this case, when the Si semiconductor layer having the same thickness as the rib portion C0 exists in the region in close proximity to the rib portion C0 in which the light wave-guides, since the light propagating in the rib portion C0 leaks into the Si semiconductor layer having the same thickness in close proximity to the rib portion C0, the width w3 of the third slab portion C3 and the width w4 of the fourth slab portion C4 are required to be 200 nm or more in such a manner that the rib portion C0 is not positioned in close proximity to the outside Si semiconductor layer.
Examples
[0065] The MZ type optical modulator 300 was produced in a size of a cross-sectional structure of the Si semiconductor layer 403 as follows as an example, based upon the thickness t0 of the rib portion C0, the thickness t1 of the first slab portion C1, the thickness t2 of the second slab portion C2, the thickness t3 of the third slab portion C3, the thickness t4 of the fourth slab portion C4, the width w0 of the rib portion C0, the width w1 of the first slab portion C1, the width w2 of the second slab portion C2, the width w3 of the third slab portion C3 and the width w4 of the fourth slab portion C4, which were calculated as described above. In addition, the doping concentrations are as follows.
Rib Portion C0
[0066] t0=220 nm w0=500 nm
First Slab Portion C1
[0067] t1=80 nm w1=100 nm
Second Slab Portion C2
[0068] t2=80 nm w2=100 nm
Third Slab Portion C3
[0069] t3=150 nm w3>200 nm
Fourth Slab Portion C4
[0070] t4=150 nm w4>200 nm
High-Concentration p-Type Semiconductor Region 403-3
[0071] p.sup.++: 1×10.sup.20 cm.sup.−3
High-Concentration n-Type Semiconductor Region 403-4
[0072] n.sup.++: 1×10.sup.20 cm.sup.−3
Intermediate-Concentration p-Type Semiconductor Region 403-1
[0073] p.sup.+: 2.7×10.sup.17 cm
Intermediate-Concentration n-Type Semiconductor Region 403-2
[0074] n.sup.+: 3.0×10.sup.17 cm.sup.−3
[0075]
[0076]
[0077]
Second Embodiment
[0078]
[0079] In the connecting section, the width in the region of the first slab portion C1 is gradually narrower along with the waveguide direction of the light and becomes the width w1. Likewise, the width in the region of the second slab portion C2 is gradually narrower and becomes the width w2. With the connecting section formed in this manner, the mode field of the light of the rib waveguide 1003 and the optical waveguide 1023 of the phase modulation portion 1011 is gradually changed, making it possible to provide a waveguide connecting portion small in a loss. The field of the light exists in the regions leaking from the rib portion C0 in both of the phase modulation portion and the optical waveguide. Therefore, the effective refraction index of the light propagating in the optical waveguide is subjected to an influence from a refraction index of each of the third slab portion C3 and the fourth slab portion C4. By causing the third slab portion C3 and the fourth slab portion C4 to gradually approach the rib portion C0, a rapid change in the effective retraction index can be prevented to suppress the reflectance loss and the dispersion loss to be small.
[0080] Preferably an approaching method of the third slab portion C3 and the fourth slab portion C4 is to perform the approach in a ratio of a length of 10% or less to a length L long enough for the wavelength of light, such as an approach length of 1 μm to a propagation length L of 10 μm.
REFERENCE SIGNS LIST
[0081] 100, 300 MZ type phase modulator [0082] 101, 103, 104, 105, 106, 108, 123, 301, 303, 304, 305, 306, 308, 323 Optical waveguide [0083] 102, 302 Optical branching filter [0084] 107, 307 Optical multiplexer [0085] 111, 112, 311, 312 Phase modulation portion [0086] 121, 122, 124, 125, 321, 322, 324, 325 Traveling wave electrode [0087] 201, 401 Si substrate [0088] 202, 204, 205, 206, 402, 404, 405, 406 SiO.sub.2 clad layer [0089] 203, 403 Si semiconductor layer [0090] 203-3, 403-3 High-concentration p-type semiconductor region [0091] 203-4, 403-4 High-concentration n-type semiconductor region [0092] 203-1, 403-1 Intermediate-concentration p-type semiconductor region [0093] 203-2, 403-2 Intermediate-concentration n-type semiconductor region [0094] A0, C0 Rib portion [0095] A1 to A2, C1 to C4 Slab portion [0096] C Capacity [0097] R1, R2 Resistance