Electro-optical modulator and method for obtaining the same

Abstract

The present invention relates to an electro-optical modulator, in particular a bilayer graphene modulator, having an optimized arrangement to provide a large optical bandwidth and high optical transmission for light traveling through an optical waveguide (W) of the modulator, wherein at least one of a top graphene sheet (Gu) and a bottom graphene sheet (Gb) extends in the X direction: over a portion of the width of the optical waveguide (W), wherein the portion ranges from 50% to 100% of the width of the optical waveguide (W); or extends completely over the entire width of the optical waveguide (W) and extends beyond a corresponding further protruding portion, the further protruding portion having a length in the X direction of at most 25% of the width of the optical waveguide (W). The present invention also relates to a method for obtaining the electro-optical modulator of the present invention.

Description

[0001] The project that gave rise to this application has received funding from the European Union's Horizon 2020 research and innovation programme, grant agreement number 649953. Technical Field

[0002] The present invention, in a first aspect, relates generally to an electro-optic modulator, and more particularly to a double-layer graphene modulator having an optimized arrangement to provide large electro-optic bandwidth and enhanced light transmission.

[0003] A second aspect of the invention relates to a method for obtaining the electro-optical modulator of the first aspect of the invention. Background Art

[0004] An electro-optical modulator known in the prior art, in particular an electro-absorption modulator, comprises:

[0005] - semiconductor substrate;

[0006] - at least a first and a second electrode spaced apart from each other in the X direction;

[0007] an optical waveguide at least partially embedded in and / or arranged on the semiconductor substrate, the upper face of the optical waveguide being positioned at a position between, below or above the first and second electrodes along the X direction, wherein the optical waveguide extends longitudinally along a direction at least transverse (generally perpendicular) to the X direction;

[0008] a bottom graphene sheet disposed over at least a portion of the upper surface of the semiconductor substrate and extending in the X direction, a first end portion of the bottom graphene sheet being electrically connected to the first electrode, and the bottom graphene sheet not reaching the second electrode;

[0009] - a sheet of a first dielectric material extending over said bottom graphene sheet;

[0010] a top graphene sheet arranged over at least a portion of the sheet of the first dielectric material and extending in the X direction, with a first end portion electrically connected to the second electrode and without the top graphene sheet touching the first electrode; and

[0011] a second dielectric material, which is a two-dimensional material having dielectric properties at least different from the dielectric properties of the first dielectric material, covering the upper and bottom faces of the top graphene sheet and / or the upper face of the bottom graphene sheet or both.

[0012] This known electro-optical modulator theoretically provides good results with respect to its light transmission, but not with respect to its operating optical bandwidth, which can obviously be improved.

[0013] Therefore, there is a need to provide an alternative to the state of the art that covers the gaps found in the state of the art by providing an electro-optic modulator with an optimized arrangement to achieve large optical bandwidth and high optical modulation efficiency. Summary of the Invention

[0014] To this end, the present invention relates to an electro-optical modulator comprising:

[0015] - semiconductor substrate;

[0016] - at least a first and a second electrode spaced apart from each other in the X direction;

[0017] an optical waveguide at least partially embedded in and / or arranged on the semiconductor substrate, the upper face of the optical waveguide being positioned at a position between, below or above the first and second electrodes along the X direction, wherein the optical waveguide extends longitudinally along a direction at least transverse (generally perpendicular) to the X direction;

[0018] a bottom graphene sheet disposed over at least a portion of the upper surface of the semiconductor substrate and extending in the X direction, wherein a first end portion of the bottom graphene sheet is electrically connected to the first electrode and the bottom graphene sheet does not touch the second electrode;

[0019] - a sheet of a first dielectric material extending over said bottom graphene sheet;

[0020] a top graphene sheet arranged over at least a portion of the sheet of the first dielectric material and extending in the X direction, with a first end portion electrically connected to the second electrode and without the top graphene sheet touching the first electrode; and

[0021] a second dielectric material, which is a two-dimensional material having dielectric properties at least different from the dielectric properties of the first dielectric material, covering the upper and bottom faces of the top graphene sheet and / or the upper face of the bottom graphene sheet or both.

[0022] Compared to the electro-optical modulator known in the prior art, in one aspect of the present invention, it is characterized in that at least one of the top and bottom graphene sheets is oriented along the X direction:

[0023] - extends over a portion of the width of the optical waveguide, wherein said portion ranges from 50% to 100% of the width of the optical waveguide; or

[0024] Extends completely over the entire width of the optical waveguide and extends beyond a corresponding further protrusion, the length of which in the X direction is at most 25% of the width of the optical waveguide.

[0025] For one embodiment, the top graphene sheet extends completely over the entire width of the optical waveguide in the X direction and extends beyond the corresponding further protrusion by a length in the X direction of at most 25% of the width of the optical waveguide.

[0026] For another embodiment, the bottom graphene sheet extends completely over the entire width of the optical waveguide in the X direction and extends beyond the corresponding further protrusions, the length of which in the X direction is at most 25% of the width of the optical waveguide.

[0027] For a preferred embodiment, particularly when there is only one waveguide, each of the top and bottom graphene sheets meets the above requirements with respect to their extension in the X direction over a portion of the width of the optical waveguide or completely over the entire width of the optical waveguide and beyond.

[0028] For one embodiment, at least one or both of the top and bottom graphene sheets extend in the X direction over 75% to 100% of the optical waveguide width, or extend completely over the optical waveguide width and extend beyond an additional protrusion having a length of at most 25% of the optical waveguide width.

[0029] For implementations of the above embodiments, at least one of the top and bottom graphene sheets extends over 95% to 100% of the optical waveguide width in the X direction, or extends completely over the optical waveguide width and extends beyond an additional protrusion having a length of at most 5% of the optical waveguide width.

[0030] For an embodiment, at least one of the top and bottom graphene sheets extends along the X-direction over 50% to 95% of the width of the optical waveguide.

[0031] According to a preferred embodiment, the top and bottom graphene sheets extend to the same length in the X-direction.

[0032] Alternatively, the top and bottom graphene sheets have different lengths.

[0033] For one embodiment, the semiconductor substrate is covered by a thin layer called a capping layer, which is made of an oxide material such as SiO2.

[0034] One embodiment of the electro-optical modulator according to the first aspect of the present invention:

[0035] - the sheet of the first dielectric material extends in the X direction at least in the region where the top and bottom graphene sheets overlap; and

[0036] a bottom sheet of said second dielectric material covering the lower face of the top graphene sheet (when there is only a bottom sheet), or a top and bottom sheet of said second dielectric material sandwiching the top graphene sheet (when both top and bottom sheets are present), contacting the second electrode and extending in the X direction up to at least the top graphene free edge, and / or

[0037] a top sheet of a second dielectric material covering the upper face of the bottom graphene sheet (when there is only the top sheet) or top and bottom sheets of the second dielectric material sandwiching the bottom graphene sheet (when both the top and bottom sheets are present), contacting the first electrode and extending in the X direction to at least directly above (when there is only the top sheet) or directly above and directly below (when both the top and bottom sheets are present), respectively, the free edge of the bottom graphene.

[0038] There are three different implementations of this implementation:

[0039] - a sheet of the first dielectric material extends over and beyond the bottom graphene sheet in the X direction such that first and second opposing ends of the sheet of the first dielectric material contact the first and second electrodes, respectively; or

[0040] - the sheet of the first dielectric material extends in the X direction over the bottom graphene sheet until just above the free edge of the bottom graphene; or

[0041] - The sheet of the first dielectric material extends in the X direction, occupying only the aforementioned region where both the top and bottom graphene sheets overlap, ie between directly below the free edge of the top graphene and directly above the free edge of the bottom graphene.

[0042] For different implementations of the above embodiment (which can be combined with any of the three implementations described above), the top and bottom sheets of the second dielectric material sandwiching the top graphene sheet contact the second electrode and extend along the X direction directly above and directly below the top graphene, respectively, or extend to the first electrode, or to any intermediate point therebetween.

[0043] In addition, for different implementations of the above-described embodiments (which may be combined with any of the above-described implementations), the top sheet of the second dielectric material covering the upper face of the bottom graphene sheet, or the top and bottom sheets of the second dielectric material sandwiching the bottom graphene sheet, contact the first electrode and extend along the X-direction directly above and directly below the bottom graphene, respectively, or extend to the second electrode, or to any intermediate point therebetween.

[0044] According to one embodiment, with respect to the different sheets of the second dielectric material:

[0045] - the thickness of the top sheet sandwiching the top graphene sheet together with the bottom sheet is in the range of 0 to 200 nm;

[0046] - the thickness of the bottom sheet that sandwiches the bottom graphene sheet together with the top sheet is in the range of 0 nm to 10 nm; and

[0047] - the thickness of the bottom sheet that sandwiches the top graphene sheet together with the top sheet, plus the thickness of the top sheet that sandwiches the bottom graphene sheet together with the bottom sheet, is in the range of 2 nm to 40 nm.

[0048] According to an embodiment, the total dielectric thickness including the thickness of the sheet of the first dielectric material and the thickness of the second dielectric material is in the range of 9 nm to 30 nm.

[0049] For an embodiment, the thickness of the sheet of the first dielectric material is in the range of 10% to 200% of the thickness of the second dielectric material.

[0050] For a variation of the implementation, the thickness of the sheet of the first dielectric material is different from the thickness of the second dielectric material.

[0051] For some embodiments, the first dielectric material is at least one of the following materials or a combination thereof: HfO2, SiO2, Si3N4, Al2O3, ZrO2, TiO2, TiN, HfSiO4, ZrSiO4, calcium copper titanate, barium titanate, strontium titanate, barium strontium titanate, polystyrene, polypropylene, polyamide, polyethylene, and polytetrafluoroethylene.

[0052] Regarding the second dielectric material, for some embodiments it is at least one of the following two-dimensional layered materials or a combination thereof: hBN, MoTe2, WSe2, WS2, graphene, MoS2, MoSe2, WS2, WSe2, black phosphorus and SnS2.

[0053] For some embodiments, the electro-optic modulator of the present invention includes only one waveguide.

[0054] However, for other embodiments, the electro-optic modulator of the present invention includes two waveguides.

[0055] In particular, for one of these other embodiments, the electro-optical modulator according to the first aspect of the invention implements an arrangement based on a Mach-Zehnder interferometer, wherein the above-mentioned optical waveguide is a first optical waveguide branch, and the modulator further comprises:

[0056] - a second optical waveguide branch spaced apart from the first optical waveguide branch along the X direction and at least partially embedded in and / or arranged on the semiconductor substrate, wherein the second optical waveguide branch extends longitudinally along a direction at least transverse (preferably perpendicular) to the X direction; and - a third electrode spaced apart from the second electrode along the X direction, wherein an upper face of the second optical waveguide branch is positioned at a position between, below or above the second and third electrodes along the X direction.

[0057] Several different implementations of the described embodiments for realizing a Mach-Zehnder interferometer based arrangement are possible, some of which will be described below.

[0058] In particular, for one of the implementations, the electro-optic modulator further comprises:

[0059] a further bottom graphene sheet (the further bottom graphene sheet may be the same graphene sheet as the top graphene sheet covering the first optical waveguide branch, or another graphene sheet but in electrical contact with the top graphene sheet), arranged over at least a portion of the upper face of the semiconductor substrate and over at least a portion of the second optical waveguide branch and extending in the X direction;

[0060] - a further sheet of a first dielectric material extending in the X direction over the further bottom graphene sheet; and

[0061] a further top graphene sheet arranged over at least a portion of the further sheet of the first dielectric material and over at least a portion of the second optical waveguide branch and extending in the X direction; and

[0062] - further portions of a second dielectric material covering the upper and bottom faces of the further top graphene sheet and / or the upper face or the upper and bottom faces of the further bottom graphene sheet;

[0063] wherein at least one of the additional top graphene sheet and the additional bottom graphene sheet is along the X direction:

[0064] - extends over a portion of the width of the second optical waveguide branch, wherein said portion ranges from 50% to 100% of the width of the second optical waveguide branch; or

[0065] extends completely over the entire width of the second optical waveguide branch and extends beyond a respective further protruding portion, the length of the further protruding portion in the X direction being at most 25% of the width of the second optical waveguide branch.

[0066] For the above implementation variation:

[0067] a further bottom graphene sheet consisting of a protruding, stepped portion of the top graphene sheet and arranged over said portion of the upper face of the semiconductor substrate and over at least said portion of the second optical waveguide branch and extending from a first end portion of the top graphene sheet in the X direction without touching the third electrode; and

[0068] The additional top graphene sheet has a first end portion electrically connected to the third electrode and extends from the first end portion in the X direction without touching the second electrode.

[0069] For another variant of the described implementation of the arrangement embodiment based on Mach-Zehnder interferometers:

[0070] - a further bottom graphene sheet having a first end electrically connected to the third electrode and extending from the first end in the X direction over at least said portion of the upper face of the semiconductor substrate and over at least said portion of the second optical waveguide branch;

[0071] - a further sheet of the first dielectric material integral with the sheet of the first dielectric material; and

[0072] - A further top graphene sheet (which may be integral with the top graphene sheet, or a separate sheet) has a region electrically connected to the second electrode and extends from this region in the X direction without touching the third electrode.

[0073] For another variant of the implementation of the arrangement embodiment based on a Mach-Zehnder interferometer, the electro-optical modulator further comprises a fourth electrode positioned between the second and third electrodes along the X direction, wherein the upper face of the second optical waveguide branch is positioned at a position between, below, or above the fourth and third electrodes along the X direction; and wherein:

[0074] - the further bottom graphene sheet has a first end portion electrically connected to the third electrode and extends from the first end portion in the X direction over at least the portion of the upper face of the semiconductor substrate and over at least the portion of the second optical waveguide branch without touching the fourth electrode or touching the fourth electrode (in the latter case, the further bottom graphene sheet may be integral with the bottom graphene sheet or be a separate sheet);

[0075] - a further sheet of the first dielectric material integral with the sheet of the first dielectric material; and

[0076] The additional top graphene sheet has a first end portion electrically connected to the fourth electrode and extends from the first end portion in the X direction without touching the third electrode.

[0077] Combinations of two or more of any of all embodiments and implementations described in this document are accepted by the invention if these combinations are feasible and lead to working embodiments.

[0078] For example, for the arrangement implementation based on Mach-Zehnder interferometer described above and further described below, any of the embodiments and implementations explained in this document for an electro-optical modulator with only one waveguide can be applied to the arrangement implementation of the Mach-Zehnder interferometer, in particular any of the described combinations, materials, properties and dimensions of different sheets of the electro-optical modulator can be applied to different sheets arranged above and below the two waveguides of the Mach-Zehnder interferometer.

[0079] The invention also relates in a second aspect to a method for obtaining an electro-optical modulator, comprising providing and arranging each of the components of the electro-optical modulator of the first aspect of the invention according to any one of the embodiments of the invention.

[0080] For a preferred embodiment, the method of the second aspect of the present invention includes using criteria based on target optical bandwidth and target optical transmission requirements to be met by the electro-optical modulator to determine the length to be provided for:

[0081] - at least one of the top and bottom graphene sheets to extend across the width of the optical waveguide in the X direction, or to extend completely across the entire width of the optical waveguide and beyond the respective further protruding portion, and / or,

[0082] - at least one of the further top and further bottom graphene sheets to extend over the width of the second optical waveguide branch, or to extend completely over the entire width of the second optical waveguide branch and beyond the respective further protruding portion, respectively, in the X-direction.

[0083] In particular, when a larger target optical bandwidth is more desirable than a higher target optical transmission for an application, the method of the second aspect of the invention comprises, for the preferred embodiments, determining and providing those lengths such that there is less overlap between the top and bottom graphene sheets and / or between a further top and a further bottom graphene sheet.

[0084] However, when for another application a higher target light transmission is more desirable than a larger target light bandwidth, the method of the second aspect of the invention comprises, for said preferred embodiments, determining and providing those lengths such that there is a larger overlap between the top and bottom graphene sheets and / or between a further top and a further bottom graphene sheet.

[0085] A third aspect of the invention relates to a Mach-Zehnder interferometer which differs from the Mach-Zehnder interferometer-based arrangement described in this document as an embodiment of the first aspect of the invention, primarily in that for this third aspect of the invention, at least one of the top and bottom graphene sheets and / or at least one of the additional top and additional bottom graphene sheets (where those additional top and additional bottom graphene sheets are present) extends along the X direction, including but not limited to the percentage ranges described above.

[0086] In particular, a third aspect of the present invention relates to an electro-optical modulator implementing an arrangement based on a Mach-Zehnder interferometer, comprising:

[0087] - semiconductor substrate;

[0088] - at least a first and a second electrode (and optionally a third electrode, as defined in the first aspect of the invention) spaced apart from each other in the X direction;

[0089] a first optical waveguide branch embedded in and / or arranged on the semiconductor substrate, the upper face of the first optical waveguide branch being positioned at a position between the first electrode and the second electrode along the X direction, below or above the first electrode, wherein the first optical waveguide branch extends longitudinally along a direction at least transverse to the X direction;

[0090] a bottom graphene sheet arranged over at least a portion of the upper face of the semiconductor substrate and extending in the X direction, a first end portion of which is electrically connected to the first electrode, and the bottom graphene sheet does not touch the second electrode;

[0091] - a sheet of a first dielectric material extending over the bottom graphene sheet;

[0092] a top graphene sheet arranged over at least a portion of the sheet of the first dielectric material and extending along the X direction, with a first end portion electrically connected to the second electrode and the top graphene sheet not touching the first electrode;

[0093] a second dielectric material, which is a two-dimensional material having at least dielectric properties different from the dielectric properties of the first dielectric material, covering the upper and bottom faces of the top graphene sheet and / or covering the upper or both the upper and bottom faces of the bottom graphene sheet; and

[0094] a second optical waveguide branch, which is spaced apart from the first optical waveguide branch in the X direction and is embedded in and / or arranged on the semiconductor substrate, wherein the second optical waveguide branch extends longitudinally at least in a direction transverse to the X direction.

[0095] For some embodiments of the third aspect of the present invention, at least one of the top and bottom graphene sheets and / or at least one of the additional top and additional bottom graphene sheets is along the X direction:

[0096] - extends over a portion of the width of the respective (first or second) optical waveguide branch, wherein said portion ranges from 1% to almost 100% of the width of the respective (first or second) optical waveguide branch; or

[0097] - extends over 100% of the width of the respective (first or second) optical waveguide branch; or

[0098] - extends completely over the entire width of the respective (first or second) optical waveguide branch and extends beyond the respective further protruding portion, the length of which in the X direction is at most 100% (or even more) of the width of the respective (first or second) optical waveguide branch. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Hereinafter, some preferred embodiments of the present invention will be described with reference to the accompanying drawings, which are provided for illustrative purposes only and do not limit the scope of the present invention.

[0100] Figure 1 The electro-optic modulator of the first aspect of the invention is schematically shown in perspective view, for example in which it comprises only one waveguide and shows the obtained light transmission as a function of the voltage (V SD ), where β represents the modulator efficiency and hω represents the incident light.

[0101] Figure 2 The electro-optic modulator of the first aspect of the present invention is schematically shown in a side cross-sectional view, and is used for Figure 1 An embodiment similar to the embodiment of .

[0102] Figure 3 shows a graph of light transmission versus voltage, involving Figure 1 and Figure 2 An electro-optic modulator (wherein a voltage is applied between the first and second electrodes, ie, V SD ), but for different “graphene stretching” (these terms will be described below).

[0103] Figure 4 shows the relationship between bandwidth and "graphene broadening" for different contact resistivities, also involving Figure 1 and Figure 2 electro-optic modulator.

[0104] Figure 5A graph showing the relationship between light transmission and voltage for different thicknesses of the top sheet (M4) of the second dielectric material is also shown. Figure 1 and Figure 2 An electro-optic modulator (wherein a voltage is applied between the first and second electrodes, ie, V SD ).

[0105] Figure 6 A graph showing the relationship between light transmission and voltage for different thicknesses of the bottom sheet (M1) of the second dielectric material is also shown. Figure 1 and Figure 2 An electro-optic modulator (wherein a voltage is applied between the first and second electrodes, ie, V SD ), including the case of zero thickness waveform, i.e. for Figure 1 and Figure 2 The case of the electro-optic modulator shown in , but modified so as not to include the bottom sheet (M1).

[0106] Figure 7 A graph showing the relationship between light transmission and voltage for different percentages of sheet (DS) thickness of the first dielectric material is also provided. Figure 1 and Figure 2 An electro-optic modulator (wherein a voltage is applied between the first and second electrodes, ie, V SD ).

[0107] Figure 8 Graphs showing light transmission versus voltage for different combinations of sheets of first and second dielectric materials and corresponding thicknesses are also provided. Figure 1 and Figure 2 An electro-optic modulator (wherein a voltage is applied between the first and second electrodes, ie, V SD ), which does not include the top sheet (M4) and the bottom sheet (M1) of the second dielectric material, i.e. Figure 1 and Figure 2 The case of the electro-optic modulator shown in , but modified so as not to include one of the sheets (M4 or M1).

[0108] Figure 9 shows a graph of light transmission versus voltage for different thicknesses of the entire dielectric material, i.e., M3, M2, and DS layers, between the top and bottom graphene sheets. Figure 1 and Figure 2 An electro-optic modulator (wherein a voltage is applied between the first and second electrodes, ie, V SD ).

[0109] Figures 10a to 10e Different variants and / or implementations of an embodiment are schematically shown, in which the electro-optical modulator according to the first aspect of the invention implements an arrangement based on a Mach-Zehnder interferometer. Figures 10a to 10eThe arrangement depicted in also represents an embodiment of the third aspect of the invention. DETAILED DESCRIPTION

[0110] In this section, some working embodiments of the electro-optical modulator according to the first aspect of the present invention will be described with reference to the accompanying drawings.

[0111] Specifically, in Figure 1 and Figure 2 An embodiment in which the modulator has only one waveguide is disclosed in Figures 10a to 10e Embodiments are disclosed in which the modulator has two waveguides, in particular in order to realize different arrangements based on Mach-Zehnder interferometers.

[0112] like Figure 1 and Figure 2 As shown, for the embodiment illustrated therein, the electro-optic modulator comprises:

[0113] - a semiconductor substrate S, which is usually covered by a thin layer (typically about 20 nm thick) called a capping layer (not shown), made of an oxide material such as SiO2;

[0114] - a first electrode E1 and a second electrode E2, which are spaced apart from each other along the X direction (see Figure 2 ), and undergo Figure 1 The drain-source voltage shown;

[0115] an optical waveguide W embedded in the semiconductor substrate S, with its upper surface flush with the upper surface of the semiconductor substrate S (although the modulator should function properly if it is not flush), wherein, for the illustrated embodiment, the upper surface of the optical waveguide W is positioned directly below a position between the first electrode E1 and the second electrode E2 along the X direction, wherein the optical waveguide W extends longitudinally along a direction transverse to (preferably perpendicular to) the X direction;

[0116] a bottom graphene sheet Gb, arranged over a portion of the upper surface of the semiconductor substrate S and extending in the X direction over the portion, with a first end portion electrically connected to the first electrode E1 and the bottom graphene sheet Gb not touching the second electrode E2;

[0117] a sheet DS of a first dielectric material extending over the bottom graphene sheet Gb, contacting both the first electrode E1 and the second electrode E2;

[0118] a top graphene sheet Gu arranged over a portion of the sheet DS of the first dielectric material and extending in the X direction over the portion, a first end portion of which is electrically connected to the second electrode E2 and the top graphene sheet Gu does not touch the first electrode E1; and

[0119] a second dielectric material having dielectric properties at least different from those of the first dielectric material, covering the upper and bottom faces of the top graphene sheet Gu and / or the upper face or the upper and bottom faces of the bottom graphene sheet Gb.

[0120] For the illustrated embodiment, each of the top graphene sheet Gu and the bottom graphene sheet Gb extends completely across the entire width of the optical waveguide W in the X direction and extends beyond a corresponding further protruding portion, identified with reference numerals pu and pb, respectively.

[0121] Each of these protruding portions pu, pb has a length in the X direction of up to 25% of the width of the optical waveguide W, identified by reference symbol "a". Figure 2 In the diagram, the protruding parts pu, pb appear to be longer, but this is only a schematic diagram and cannot be used to extract a teaching about the dimensions based on the measurements therein. In fact, the protruding parts pu, pb have a length of up to 25% of the width "a".

[0122] Alternatively, for non-illustrated embodiments, each of the top graphene sheet Gu and the bottom graphene sheet Gb extends over only a portion of the width of the optical waveguide W in the X direction, specifically, over a portion ranging from 50% to 100% of the width “a” of the optical waveguide W.

[0123] In this document, and in particular Figure 3 and Figure 4 In the diagrams of FIG, the term “graphene stretching” has been used to refer to the above-mentioned extension of the top graphene sheet Gu and the bottom graphene sheet Gb along the X-direction, but in this case for the width “a” of the optical waveguide W to be an absolute value of 1 μm (i.e. not in percentage terms).

[0124] In particular, positive values ​​of "graphene broadening" correspond to the aforementioned values ​​of the length of each of the protrusions pu and pb. A waveform with a "graphene broadening" of 1000 nm (i.e., for a protrusion with a length of 100% of the width "a") is shown; this waveform is not part of the present invention but is depicted only for comparison purposes with the remaining waveforms.

[0125] Negative "graphene stretching" values ​​relate to the embodiment described above in which each of the top graphene sheet Gu and the bottom graphene sheet Gb extends along the X-direction over only a portion ranging from 50% to 100% of the width a of the optical waveguide W. Specifically, each negative value corresponds to the length, measured along the X-direction, of the distance between the free edge of the corresponding graphene sheet (top Gu or bottom Gb) and the edge of the waveguide W toward which the graphene sheet extends but does not reach. In other words, for a width "a" of 1 μm, a "graphene stretching" of -225 nm corresponds to a portion of 77.5% of the width "a" along which the corresponding graphene sheet extends in the X-direction.

[0126] By comparison Figure 3 and Figure 4 From the graphical results, one can see how slightly changing the "graphene stretching" has a large effect on increasing the operating optical bandwidth while only slightly decreasing the light transmission.

[0127] The present inventors have found that this is because the area where the top graphene sheet Gu and the bottom graphene sheet Gb overlap has a capacitance C that is proportional to its size. The bandwidth of the modulator is defined as BW = 1 / 2πRC. The smaller the overlap between the top graphene sheet Gu and the bottom graphene sheet Gb, the lower C, thereby increasing the bandwidth (this is in Figure 4 On the other hand, the lower the C, i.e. the smaller the overlap area, the worse the transmission (e.g. Figure 3 shown).

[0128] Figure 3 and Figure 4 charts, and Figure 5 、 Figure 6 、 Figure 7 and Figure 8 The graphs are obtained by numerical simulation of an electro-optic modulator where the first dielectric material is HfO2 and the second electro-optic material is hBN. However, similar results can be obtained for other types of dielectric materials, such as those cited in the previous section of this document.

[0129] for Figure 1 and Figure 2 The embodiment illustrated in

[0130] a top sheet M4 and a bottom sheet M3 of a second dielectric material sandwiching the top graphene sheet Gu, contacting the second electrode E2 and extending in the X direction to at least just above and just below the free edge of the top graphene Gu, respectively, and

[0131] - a top sheet M2 and a bottom sheet M1 of a second dielectric material sandwiching the bottom graphene sheet Gb, contacting the first electrode E1 and extending in the X direction up to just above and just below the free edge of the bottom graphene Gb, respectively.

[0132] Figure 5 and Figure 6 The graphs show the effect of the thickness of the top sheet M4 and the thickness of the bottom sheet M1, respectively (including the case of a zero-thickness M1 sheet). The results illustrated in these graphs show that for the M4 top sheet, the thicker the better, while for the M1 bottom sheet, the thinner the better.

[0133] The influence of the thickness of the sheet DS of the first dielectric material on Figure 7 , where the first dielectric material is HfO2. The total thickness of the dielectric sheets (all dielectric sheets, sheets of the first dielectric material, and sheets of the second dielectric material) remains constant, such that as the thickness of HfO2 increases, the thickness of sheets M2 and / or M3 decreases proportionally. The results show that for DS sheets, a higher percentage is better.

[0134] Figure 8 It shows how the order of the different dielectric sheets within the top and bottom graphene sheets (only M3, M2 and DS are considered) has no effect on the light transmission. This is due to the fact that in the simulations, M1 and M2 are the same material and it is their total thickness that matters.

[0135] The effect of dielectric material thickness in the top and bottom graphene sheets (M3+M2+DS) is Figure 9 As shown in FIG, the smaller the thickness, the better. The relative thickness (percentage) of each dielectric sheet remains unchanged.

[0136] The thickness of the entire dielectric material (M1+M2+M3+M4+DS) affects Figure 9 The relative thickness (percentage) of each dielectric sheet remains constant.

[0137] Figures 10a to 10e Different variants and / or implementations of an embodiment are schematically shown, wherein the electro-optical modulator according to the first aspect of the invention implements an arrangement based on a Mach-Zehnder interferometer ( Figures 10a to 10e The arrangement depicted in also represents an embodiment of the third aspect of the invention), wherein the optical waveguide W is a first optical waveguide branch W1, and the modulator further comprises:

[0138] a second optical waveguide branch W2 spaced apart from the first optical waveguide branch W1 in the X direction and embedded in the semiconductor substrate S, wherein the second optical waveguide branch W2 extends longitudinally in a direction at least transverse to the X direction; and

[0139] a third electrode E3 spaced apart from the second electrode E2 in the X direction, wherein, for the illustrated embodiment, the upper face of the second optical waveguide branch W2 is positioned below a position between said second and third electrodes E2 and E3 in the X direction.

[0140] for Figure 10a In the variant shown in , the second optical waveguide branch W2 is left uncovered, but embedded in the substrate S. Therefore, in use, i.e. when a voltage V1 is applied between the first electrode E1 and the second electrode E2, only the phase of the light propagating through the core of the first optical waveguide branch W1 is changed.

[0141] For the remaining variants, i.e. Figures 10b to 10e In a variation of the present invention, when in use, the phase of light propagating through the cores of the two optical waveguide branches W1 and W2 is changed, and the electro-optic modulator further includes:

[0142] a further bottom graphene sheet Gbf arranged over at least a portion of the upper face of the semiconductor substrate S and over at least a portion of the second optical waveguide branch W2 and extending in the X direction over said portions;

[0143] a further sheet DSf of said first dielectric material extending in the X direction above the further bottom graphene sheet Gbf;

[0144] a further top graphene sheet Guf arranged over at least a portion of the further sheet of first dielectric material DSf and extending in the X direction in front of and over at least a portion of the second optical waveguide branch W2; and

[0145] - further portions of a second dielectric material covering the upper and bottom faces of the further top graphene sheet Guf and / or the upper face or the upper and bottom faces of the further bottom graphene sheet Gbf.

[0146] One or both of the additional top graphene sheet Guf and the additional bottom graphene sheet Gbf are along the X direction:

[0147] - extends over a portion of the width of the second optical waveguide branch W2, wherein said portion ranges from 50% to 100% of the width of the second optical waveguide branch W2; or

[0148] extends completely over the entire width of the second optical waveguide branch W2 and extends beyond a corresponding further protruding portion, the length of which in the X direction is at most 25% of the width of the second optical waveguide branch W2.

[0149] Specifically, for Figure 10b and Figure 10c Illustrated variations:

[0150] a further bottom graphene sheet Gbf having a first end electrically connected to the third electrode E3 and extending from this first end in the X direction over only a portion of the upper face of the semiconductor substrate S and, in this case, over the entire width of the second optical waveguide branch W2 and beyond the corresponding further protruding portion, the length of this further protruding portion in the X direction being at most 25% of the width of the second optical waveguide branch W2, although, as mentioned above, it may extend over only a portion ranging from 50% to 100% of this width;

[0151] - said further sheet DSf of said first dielectric material is integral with said sheet DS of said first dielectric material; and

[0152] - the further top graphene sheet Guf has a first end electrically connected to the second electrode E2 and extends from this first end in the X direction without touching the third electrode E3, in this case extending over the entire width of the second optical waveguide branch W2 and beyond (up to 25% of its width), although as mentioned above, it may extend over only a portion ranging from 50% to 100% of this width.

[0153] Alternatively, for non-illustrated embodiments, each of the top graphene sheet Gu and the bottom graphene sheet Gb extends over only a portion of the width of the second optical waveguide branch W2 in the X direction, specifically over a portion ranging from 50% to 100% of the width of the second optical waveguide branch W2.

[0154] Figure 10b and Figure 10c The only difference between the variants is the electrodes to which the terminals of the voltage source V1 are applied, since the voltage source V2 is applied to the same electrodes for both figures. Figure 10b , the voltage V1 is applied to the second electrode E2, while the first electrode E1 is connected to the ground, and for Figure 10c The connection is reversed.

[0155] for Figure 10d In the illustrated variation, the electro-optical modulator further includes a fourth electrode E4 positioned between the second electrode E2 and the third electrode E3 along the X direction, wherein the upper surface of the second optical waveguide branch W2 is positioned below a position between the fourth electrode E4 and the third electrode E3 along the X direction; and wherein:

[0156] - a further bottom graphene sheet Gbf integral with the bottom graphene sheet Gb, such that opposite ends of the formed common graphene sheet are electrically connected to the first electrode E1 and the third electrode E3, respectively, extending in the X direction above the upper face of the substrate S and over the entire width of both the first optical waveguide branch W and the second optical waveguide branch W2;

[0157] - a further sheet DSf of a first dielectric material integral with the sheet DS of the first dielectric material; and

[0158] - the further top graphene sheet Guf has a first end portion electrically connected to the fourth electrode E4 and extends from this first end portion in the X direction without touching the third electrode E3, in this case over the entire width of the second optical waveguide branch W2 and beyond (up to 25% of its width), although as mentioned above it may extend over only a portion ranging from 50% to 100% of this width.

[0159] for Figure 10d The voltage sources V1 and V2 are connected in the same way as Figure 10b The connection method is the same.

[0160] like Figure 10e As shown, for the variant exemplified there:

[0161] a further bottom graphene sheet Gbf having a first end electrically connected to the third electrode E3 and extending from this first end in the X direction over a portion of the upper face of the semiconductor substrate S and, in this case, over the entire width of the second optical waveguide branch W2 and beyond (up to 25% of its width), although, as mentioned above, it may extend over only a portion ranging from 50% to 100% of this width;

[0162] a further sheet DSf of a first dielectric material being integral with the sheet DS of the first dielectric material and the common sheet thus created extending from the first electrode E1 to the third electrode E3 ; and

[0163] - the additional top graphene sheet Guf is integral with the top graphene sheet Gu, so that the central region of the resulting common graphene sheet is electrically connected to the second electrode E2, and the two opposite ends extend in the X direction above the upper face of the substrate S towards the first electrode E1 and the third electrode E3, respectively, so that, in this case, Gu and Guf each extend over and beyond the entire width of the first optical waveguide branch W1 or the second optical waveguide branch W2 (at most 25% of its width), although as mentioned above, it can extend over only a portion ranging from 50% to 100% of this width.

[0164] for Figure 10eIn a variation of the embodiment, three voltages, namely, V1, V2, and V3, are applied to corresponding electrodes among the first electrode E1, the second electrode E2, and the third electrode E3, respectively.

[0165] As mentioned above, Figures 10a to 10e are schematic, meaning that, for example, elements depicted as suspended are not suspended but are actually bent.

[0166] Figures 10a to 10e The operation of the modulator is known in connection with an arrangement based on a Mach-Zehnder interferometer, and for Figure 1 and Figure 2 The modulator has been explained above, i.e. it benefits from the same effect explained above regarding “graphene broadening”.

[0167] Those skilled in the art may introduce variations and modifications in the described embodiments without departing from the scope of the invention as defined in the accompanying claims.

Claims

1. An electro-optical modulator, comprising: - a semiconductor substrate (S); - at least a first electrode (E1) and a second electrode (E2) spaced apart from each other along the X direction; - an optical waveguide (W) embedded in and / or arranged on the semiconductor substrate (S), the upper face of the optical waveguide (W) being positioned at a position between, below or above the first electrode (E1) and the second electrode (E2) along the X direction, wherein the optical waveguide (W) extends longitudinally along a direction at least transverse to the X direction; a bottom graphene sheet (Gb) arranged above at least a portion of the upper surface of the semiconductor substrate (S) and extending along the X direction, wherein a first end of the bottom graphene sheet is electrically connected to the first electrode (E1) and the bottom graphene sheet (Gb) does not touch the second electrode (E2); - a sheet of a first dielectric material (DS) extending above said bottom graphene sheet (Gb); a top graphene sheet (Gu) arranged over at least a portion of the sheet (DS) of the first dielectric material and extending along the X direction, wherein a first end of the top graphene sheet is electrically connected to the second electrode (E2) and the top graphene sheet (Gu) does not touch the first electrode (E1); and - a second dielectric material, said second dielectric material being a two-dimensional material having dielectric properties at least different from the dielectric properties of said first dielectric material, Characterized in that the second dielectric material covers the upper surface and the bottom surface of the top graphene sheet (Gu) and / or covers both the upper surface and the bottom surface of the bottom graphene sheet (Gb); and At least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) is along the X direction: - extends over a portion of the width of the optical waveguide (W), wherein the portion ranges from 50% to 100% of the width of the optical waveguide (W); or - a respective further protrusion extending completely over the entire width of the optical waveguide (W) and extending beyond its length in the X direction by at most 25% of the width of the optical waveguide (W).

2. The electro-optic modulator according to claim 1, wherein The top graphene sheet (Gu) extends completely over the entire width of the optical waveguide (W) in the X direction and extends beyond its respective further protruding portion by a length in the X direction of at most 25% of the width of the optical waveguide (W).

3. The electro-optic modulator according to claim 1, wherein The bottom graphene sheet (Gb) extends completely over the entire width of the optical waveguide (W) in the X direction and extends beyond its corresponding further protrusion by a length in the X direction of at most 25% of the width of the optical waveguide (W).

4. The electro-optic modulator according to claim 1, wherein Each of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) extends over a portion of the width of the optical waveguide (W) along the X direction, wherein the portion ranges from 50% to 100% of the width of the optical waveguide (W).

5. The electro-optic modulator according to claim 1, wherein Each of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) extends completely over the entire width of the optical waveguide (W) in the X-direction and extends beyond its respective further protruding portion by a length in the X-direction of at most 25% of the width of the optical waveguide (W).

6. The electro-optic modulator according to claim 1, wherein At least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) extends over 75% to 100% of the width of the optical waveguide (W) along the X-direction.

7. The electro-optic modulator according to claim 6, wherein At least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) extends over 95% to 100% of the width of the optical waveguide (W) along the X-direction.

8. The electro-optic modulator according to claim 1, wherein At least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) extends over 50% to 95% of the width of the optical waveguide (W) along the X direction.

9. The electro-optic modulator according to claim 1, wherein At least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) extends completely over the width of the optical waveguide (W) in the X direction and extends beyond a further protruding portion having a length of at most 5% of the width of the optical waveguide (W).

10. The electro-optic modulator of claim 1 , wherein: - the sheet of the first dielectric material (DS) extends in the X direction at least in the region where the top graphene sheet (Gu) and the bottom graphene sheet (Gb) overlap; and - a third bottom sheet (M3) of the second dielectric material covering the lower face of the top graphene sheet (Gu) or a fourth top sheet (M4) and a third bottom sheet (M3) sandwiching the top graphene sheet (Gu), contacting the second electrode (E2) and extending in the X direction to at least directly above and directly below the free edge of the top graphene sheet (Gu), respectively, and / or - a second top sheet (M2) of the second dielectric material covering the upper surface of the bottom graphene sheet (Gb), or the second top sheet (M2) and the first bottom sheet (M1) of the second dielectric material sandwiching the bottom graphene sheet (Gb), contacting the first electrode (E1) and extending along the X direction to at least directly above or directly above and directly below the free edge of the bottom graphene sheet (Gb).

11. The electro-optic modulator according to claim 10, wherein Regarding the different sheets of the second dielectric material: - a fourth top sheet (M4) sandwiching the top graphene sheet (Gu) together with the third bottom sheet (M3) has a thickness ranging from 0 nm to 200 nm; - the thickness of the first bottom sheet (M1) sandwiching the bottom graphene sheet (Gb) together with the second top sheet (M2) is in the range of 0 nm to 10 nm; and - the thickness of the third bottom sheet (M3) that sandwiches the top graphene sheet (Gu) together with the fourth top sheet (M4), plus the thickness of the second top sheet (M2) that sandwiches the bottom graphene sheet (Gb) together with the first bottom sheet (M1), is in the range of 2nm to 40nm.

12. The electro-optic modulator according to claim 1, wherein The total dielectric thickness, including the thickness of the sheet (DS) of the first dielectric material and the thickness of the second dielectric material, is in the range of 9 nm to 30 nm.

13. The electro-optic modulator according to claim 1, wherein The thickness of the sheet (DS) of the first dielectric material is in the range of 10% to 200% with respect to the thickness of the second dielectric material.

14. The electro-optic modulator according to claim 13, wherein The sheet (DS) of the first dielectric material has a thickness that is different from the thickness of the second dielectric material.

15. The electro-optic modulator of claim 1 , wherein: The first dielectric material is at least one of the following materials or a combination thereof: HfO2, SiO2, Si3N4, Al2O3, ZrO2, TiO2, TiN, HfSiO4, ZrSiO4, calcium copper titanate, barium titanate, strontium titanate, barium strontium titanate, polystyrene, polypropylene, polyamide, polyethylene and polytetrafluoroethylene; and The second dielectric material is at least one of the following two-dimensional layered materials or a combination thereof: hBN, MoTe2, WSe2, WS2, MoS2, MoSe2, WS2, WSe2, black phosphorus and SnS2.

16. The electro-optic modulator of claim 1 , wherein: The first dielectric material is at least one of the following materials or a combination thereof: HfO2, SiO2, Si3N4, Al2O3, ZrO2, TiO2, TiN, HfSiO4, ZrSiO4, calcium copper titanate, barium titanate, strontium titanate, barium strontium titanate, polystyrene, polypropylene, polyamide, polyethylene and polytetrafluoroethylene; and The second dielectric material is at least two of the following two-dimensional layered materials or a combination thereof: hBN, MoTe2, WSe2, WS2, graphene, MoS2, MoSe2, WS2, WSe2, black phosphorus and SnS2.

17. The electro-optic modulator according to claim 1, which implements an arrangement based on a Mach-Zehnder interferometer, wherein: The optical waveguide (W) is a first optical waveguide branch (W1), and the modulator further comprises: a second optical waveguide branch (W2) spaced apart from the first optical waveguide branch (W1) along the X direction and embedded in and / or arranged on the semiconductor substrate (S), wherein the second optical waveguide branch (W2) extends longitudinally along a direction at least transverse to the X direction; and - a third electrode (E3) spaced apart from the second electrode (E2) along the X direction, wherein the upper face of the second optical waveguide branch (W2) is positioned at a position between, below, or above the second electrode (E2) and the third electrode (E3) along the X direction.

18. The electro-optic modulator of claim 17 , further comprising: a further bottom graphene sheet (Gbf) arranged over at least a portion of the upper face of the semiconductor substrate (S) and over at least a portion of the second optical waveguide branch (W2) and extending in the X direction; - a further sheet (DSf) of said first dielectric material extending in said X direction over said further bottom graphene sheet (Gbf); a further top graphene sheet (Guf) arranged over at least a portion of said further sheet of said first dielectric material (DSf) and over at least a portion of said second optical waveguide branch (W2) and extending in said X direction; as well as - further portions of the second dielectric material covering the upper and bottom faces of the further top graphene sheet (Guf) and / or covering the upper or upper and bottom faces of the further bottom graphene sheet (Gbf); wherein at least one of the further top graphene sheet (Guf) and the further bottom graphene sheet (Gbf) is along the X direction: - extends over a portion of the width of the second optical waveguide branch (W2), wherein the portion ranges from 50% to 100% of the width of the second optical waveguide branch (W2); or a respective further protrusion extending completely over the entire width of the second optical waveguide branch (W2) and extending beyond its length in the X direction by at most 25% of the width of the second optical waveguide branch (W2).

19. The electro-optic modulator of claim 18, wherein: - the further bottom graphene sheet (Gbf) has a first end portion electrically connected to the third electrode (E3) and extends from the first end portion along the X direction over at least the portion of the upper face of the semiconductor substrate (S) and over at least the portion of the second optical waveguide branch (W2); - said further sheet (DSf) of said first dielectric material is integral with said sheet (DS) of said first dielectric material; and - the further top graphene sheet (Guf) has a region electrically connected to the second electrode (E2) and extends from the region in the X direction without touching the third electrode (E3).

20. The electro-optic modulator of claim 18, further comprising a fourth electrode (E4) positioned between the second electrode (E2) and the third electrode (E3) along the X direction, wherein The upper surface of the second optical waveguide branch (W2) is positioned at, below, or above a position between the fourth electrode (E4) and the third electrode (E3) along the X direction; and in: - the further bottom graphene sheet (Gbf) has a first end portion electrically connected to the third electrode (E3) and extends from the first end portion of the further bottom graphene sheet in the X direction over at least the portion of the upper face of the semiconductor substrate (S) and over at least the portion of the second optical waveguide branch (W2); - said further sheet (DSf) of said first dielectric material is integral with said sheet (DS) of said first dielectric material; and The further top graphene sheet (Guf) has a first end portion electrically connected to the fourth electrode (E4) and extends from the first end portion of the further top graphene sheet in the X direction without touching the third electrode (E3).

21. A method for obtaining an electro-optical modulator, comprising providing and arranging each of the components of an electro-optical modulator according to any of the preceding claims 1 to 17.

22. The method of claim 21 , comprising using criteria based on target optical bandwidth and target optical transmission requirements to be met by the electro-optical modulator to determine the length to be provided to: - at least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) is configured to extend over the width of the optical waveguide (W) along the X direction, or to extend completely over the entire width of the optical waveguide (W) and extend beyond the corresponding further protruding portion.

23. A method for obtaining an electro-optical modulator, comprising providing and arranging each of the components of an electro-optical modulator according to any of the preceding claims 18 to 20.

24. The method of claim 23, comprising using criteria based on target optical bandwidth and target optical transmission requirements to be met by the electro-optical modulator to determine the length to be provided to: - at least one of the top graphene sheet (Gu) and the bottom graphene sheet (Gb) to extend over the width of the optical waveguide (W) along the X direction, or to extend completely over the entire width of the optical waveguide (W) and beyond the respective further protruding portion, and / or, - at least one of the further top graphene sheet (Guf) and the further bottom graphene sheet (Gbf) to extend over the width of the second optical waveguide branch (W2) along the X direction, or to extend completely over the entire width of the second optical waveguide branch (W2) and beyond the respective further protruding portion.

Images