Ray Tracing Modeling of Electromagnetic Propagation for On-Chip Wireless Optical Communications

Journal of Low Power Electronics and Applications

Article Ray Tracing Modeling of Electromagnetic Propagation for On-Chip Wireless Optical Communications

Franco Fuschini 1,* , Marina Barbiroli 1, Marco Zoli 1, Gaetano Bellanca 2, Giovanna Calò 3 , Paolo Bassi 1 and Vincenzo Petruzzelli 3

1 Department of Electrical, Electronic and Information Eng. “G. Marconi”, University of Bologna, 40136 Bologna, Italy; [email protected] (M.B.); [email protected] (M.Z.); [email protected] (P.B.) 2 Department of Engineering, University of Ferrara, 44122 Ferrara, Italy; [email protected] 3 Department of Electrical and Information Engineering, Polytechnic of Bari, 70126 Bari, Italy; [email protected] (G.C.); [email protected] (V.P.) * Correspondence: [email protected]; Tel.: +39-051-209-3437

Received: 13 September 2018; Accepted: 12 October 2018; Published: 17 October 2018

Abstract: Multi-core processors are likely to be a point of no return to meet the unending demand for increasing computational power. Nevertheless, the physical interconnection of many cores might currently represent the bottleneck toward kilo-core architectures. Optical wireless networks on-chip are therefore being considered as promising solutions to overcome the technological limits of wired interconnects. In this work, the spatial properties of the on-chip wireless channel are investigated through a ray tracing approach applied to a layered representation of the chip structure, highlighting the relationship between path loss, antenna positions and radiation properties.

Keywords: electromagnetic propagation; ray tracing; optical wireless network on chip

1. Introduction The computation hunger affecting technological progress has fostered the development of multi-core architectures, where data processing is simultaneously carried out by several processors (or cores) embedded in the same processor die, thus dramatically reducing the computational effort. Since mutual interactions among the cores are necessary, they must be effectively interconnected. To this aim, traditional bus architectures have been replaced by networks on chip (NoC), where the processor chip includes electrical wires and routers besides cores and cache banks [1,2]. Nonetheless, interconnect issues such as layout complexity, high latency, and power consumption are far from being completely solved, to the extent that they might seriously thwart further evolution towards kilo-core architectures [3]. In particular, electrical wires undergo propagation delays and losses which do not scale down at the same rate as transistors, and they can hardly support the high data-rate required by core-to-core communications [2,4]. These issues can be partly tackled by optical networks on chip (ONoC) [4,5], which take advantage of optical interconnects to provide high-speed communications (also exploiting wavelength division multiplexing) with lower propagation delays and weaker propagation losses. Nonetheless, on-chip integration of optical sources still undergoes several technological limitations [5], e.g., related to the laser efﬁciency, which reduces as the chip temperature rises up and is in general quite low. On the other hand, off-chip lasers are more efﬁcient but their coupling to the chip introduces additional losses [4] and poses additional issues related to the mechanical interconnection between the source and the die. Furthermore, important optical devices like micro-rings require extra-power expenditure to compensate for the resonant wavelength shift due to manufacturing geometric inaccuracies [4]. Finally,

J. Low Power Electron. Appl. 2018, 8, 39; doi:10.3390/jlpea8040039 www.mdpi.com/journal/jlpea J. Low Power Electron. Appl. 2018, 8, 39 2 of 16 interfacing the optical network with the electrical circuitry of the cores entails some electro-optical conversion with negative effects on both energy loss/consumption and networking delays [4]. It is also worth mentioning that both electrical and optical NoC may suffer from unwanted and unpredictable cross-talk effects (especially at waveguide crossing and switching stages), which are expected to be harsher as the number of cores increases and the network layout becomes more complex. Three-dimensional circuit integration may space out interconnections, thus alleviating the cross-talk risk, but complicating the manufacturing process. In this framework, wireless networks on-chip (WiNoC) have therefore attracted increasing consideration [1,3,6] as an effective solution to provide low-latency communications and to get rid of the interconnect routing and layout complexity when a large number of cores must be arranged into the processor integrated circuit (IC) [3]. Because of the current limitations on antenna technologies, WiNoC are often investigated up to the millimeter/sub-THz bands, where on-chip antenna integration may still represent a challenge and propagation is likely to occur in near field, and possible mutual coupling might therefore arise reducing the communication efficiency [7]. Therefore, optical wireless networks on chip (OWiNoC) have been recently proposed [8], aiming at preserving the main advantages of WiNoC (low latency, simpler network layout) but fostering far-field propagation and facilitating the antenna integration process. Moreover, relying on wireless optical communications can be particularly beneficial to envisage hybrid wired/wireless optical networks, because the same wavelength propagating on optical waveguides could be directly exploited for wireless connections without any further electro-optical conversion [8]. In spite of the existing studies carried out on WiNoC, quite little consideration has been seriously devoted to wireless channel modeling [5,9,10], and hardly ever at optical frequencies [11]. In this work, the OWiNoC propagation channel is specifically investigated by means of a ray tracing (RT) approach, which is expected to be quite reliable at so large frequencies and is also inherently fit to track the multipath nature of the on-chip wireless channel. In References [9,11], the analysis is basically limited to the frequency response of the channel, whereas prediction of the spatial field distribution limited to few wavelengths is provided in Reference [10]. Conversely, the primary goal of this study is the assessment of the far-field spatial fading (which is expected to be a serious impairment in the optical frequency range) and of the maximum communication distance for different chip structures. Moreover, the impact of the antenna position and radiation properties is here discussed to some extent in several reference cases, whereas oversimplified radiators in a single case study are considered in References [10,11]. The paper is organized as follows: Section2 provides some general background about on-chip wireless propagation, whereas Section3 deals with the physical structure of an IC and its representation as a multi-layered medium. The RT model for on-chip propagation analysis is presented in Section4. Results of the RT simulations are discussed in Section5, and some conclusions are finally drawn in Section6.

2. Background on Propagation Mechanisms and Optical WiNoC Requirements Increasing the communication frequency in WiNoC can ease the antenna integration efforts, but also raises some propagation issues to be aware of. The communication range is always affected by the communication frequency, since greater isotropic attenuation is experienced at larger frequency as a general trend. In free space condition, the antenna gain can be easily related to the distance corresponding to the minimum required power at the receiver for a satisfactory communication by means of the Friis equation: s P 4π · d G = RX,min · (1) PTX λ where the same antennas are supposed at both link ends for the sake of simplicity, PRX,min and PTX are the receiver sensitivity and the overall transmitted power, respectively, d is the link distance and λ is J. Low Power Electron. Appl. 2018, 8, x FOR PEER REVIEW 3 of 16

PRX,min 4π ⋅d G =⋅ (1) PTX λ

where the same antennas are supposed at both link ends for the sake of simplicity, PRX,min and PTX are J.the Low receiver Power Electron. sensitivity Appl. 2018 and, 8, the 39 overall transmitted power, respectively, d is the link distance and3 of λ 16 is the wavelength of the wireless signal in the propagation medium. For instance, an antenna gain theequal wavelength to nearly of30 thedB wirelessis needed signal to convey in the a propagation power PRX,min medium. = −25 dBm For instance,to the distance an antenna d = 1 gainmm under equal free space conditions and assuming PTX = 0 dBm and λ = 1 μm. to nearly 30 dB is needed to convey a power PRX,min = −25 dBm to the distance d = 1 mm under free In spite of the tiny wavelength, the design of highly directive optical antennas is not a space conditions and assuming PTX = 0 dBm and λ = 1 µm. straightforwardIn spite of task, the tinybecause wavelength, the integration the design need pose of highlys serious directive constrains optical on the antennas size of the is on-chip not a straightforwarddevices. For instance, task, because the plasmonic the integration antennas need propos posesed serious in References constrains [8,12] on theexhibit size ofa gain the on-chip always devices.lower than For instance,10 dB, whereas the plasmonic it is increased antennas proposedto about 20 in ReferencesdB by the [8dielectric,12] exhibit solution a gain alwaysdiscussed lower in thanReference 10 dB, [13], whereas though it is at increased the expense to about of a 20quite dB bylarger the antenna dielectric size. solution Owing discussed to the current in Reference limitation [13], thoughon optical at the antenna expense gain, of a quite propagation larger antenna conditions size. Owing better tothan the currentin free limitation space would on optical be therefore antenna gain,extremely propagation beneficial conditions to the optical better wireless than in free communications. space would be Whether therefore and extremely to what beneﬁcialextent this to may the opticaloccur in wireless the on-chip communications. wireless channel Whether is investigated and to what in extentthe following this may sections. occur in In the this on-chip regard, wireless surface channelelectromagnetic is investigated waves inare the sometimes following referred sections. to In as this an regard, effective surface means electromagnetic to improve propagation waves are sometimesconditions referredcompared to to as anfree effective space [2,14,15]. means to Although improve propagationelectromagnetic conditions propagation compared is usually to free a spacethree-dimensional [2,14,15]. Although phenomenon, electromagnetic i.e., spatial propagation waves spring is usually out aof three-dimensional the transmitting phenomenon,antenna and i.e.,spread spatial over waves the full spring space out interacting of the transmitting with the items antenna all around, and spread surface over waves the full might space be interacting triggered withunder the particular items all around,circumstances surface and waves travel might close be triggeredto the chip under surface particular (and circumstancestherefore in two and spatial travel closedimensions) to the chip between surface different (and therefore cores (Figure in two spatial1). Sinc dimensions)e the surface between wave is different confined cores at the (Figure planar1). Sinceinterface, the surfaceits wavefronts wave is conﬁnedundergo ata smaller the planar spatial interface, broadening its wavefronts compared undergo to a spatial a smaller wave, spatial and broadeningtherefore the compared corresponding to a spatial path loss wave, would and increase therefore proportionally the corresponding to the pathlink distance loss would d instead increase of 2 proportionallyd as in free space to the [2]. link distance d instead of d2 as in free space [2].

Figure 1. Sketch of the spatial and surface wave concepts. Figure 1. Sketch of the spatial and surface wave concepts. In order to take full advantage of surface propagation, surface waves only should be excited. The launchingIn order to efficiency take full ofadvantage a surface of wave surface is oftenpropagation, defined surface as the ratiowaves between only should the surface be excited. and theThe overall launching radiated efficiency power of [a16 surface]. Design wave of effectiveis often defined surface as wave the antennasratio between has beenthe surface dealt with and forthe quiteoverall a longradiated time: power investigations [16]. Design carried of effective out on su differentrface wave surface antennas wave has launchers been dealt in Reference with for quite [17] pointeda long time: out that investigations efficiency nearly carried equal out on to 100%different could surface be easily wave achieved launchers in theory, in Reference but not [17] as much pointed in practice.out that Moreover,efficiency nearly theoretical equal analysis to 100% in thecould mm-wave be easily band achieved [10] highlighted in theory, thatbut not the roleas much played in bypractice. spatial/surface Moreover, propagation theoretical analysis is greatly in affected the mm-wa by frequency,ve band [10] material highlighted properties, that andthe role position played of theby spatial/surface antennas within propagation the on-chip is wirelessgreatly affected channel. by Finally, frequency, surface material wave prop interconnectserties, and represent position of a sortthe ofantennas emerging within solution the on-chip currently wireless under investigationchannel. Finally, mainly surface at millimeter wave interconnects frequencies represent [2], and no a significantsort of emerging studies solution have so currently far addressed under design investigation challenges mainly for integrated at millimeter surface frequencies wave launchers [2], and no in thesignificant optical range.studies have so far addressed design challenges for integrated surface wave launchers in the opticalSoothing range. the debate on whether optical WiNoC should better rely on spatial or surface propagation is farSoothing beyond the the scope debate of this on work.whether Here, optical possible WiNoC surface should propagation better effectsrely on are spatial simply or neglected surface atpropagation the moment is andfar thebeyond main the goal scope is the of investigation this work. Here, of the possible fading properties surface propagation of the on-chip effects spatial are radio channel.

3. General Description of the Multi-Core Chip Structure As a matter of fact, wireless propagation is quite sensitive to the properties of the environment where it takes place. Therefore, the ﬁrst step for the electromagnetic characterization of the wireless J. Low Power Electron. Appl. 2018, 8, x FOR PEER REVIEW 4 of 16

simply neglected at the moment and the main goal is the investigation of the fading properties of the on-chip spatial radio channel.

3. General Description of the Multi-Core Chip Structure

J. Low PowerAs a Electron.matter Appl.of fact,2018 wireless, 8, 39 propagation is quite sensitive to the properties of the environment4 of 16 where it takes place. Therefore, the first step for the electromagnetic characterization of the wireless channel always consists of its physical description. A very detailed and precise representation channelusually alwaysyields consistsa deeper of itsinsight physical but description. is often limited A very detailedto the specific and precise case representation under investigation. usually yieldsConversely, a deeper limiting insight the but description is often limitedof the scenario to the specificto the features case under mainly investigation. affecting electromagnetic Conversely, limitingpropagation the description may result ofin the prediction scenario still to the reliable features in many mainly different affecting cases, electromagnetic provided that propagation they share maythe same result macro in prediction structure. still According reliable into manythe latter different approach, cases, this provided section thataims they at identifying share the samesome macrocommon structure. characteristics According underlying to the latter any approach,multi-core this IC, section in order aims to atdefine identifying some reference some common input characteristicslayouts for the underlying ray tracing anypropagation multi-core analysis IC, in ordercarried to out define in Section some reference 5. input layouts for the ray tracingWith reference propagation to the analysis complementary carried out metal-oxide in Section5. semiconductor (CMOS) technology, an IC is alwaysWith achieved reference from to thea silicon complementary wafer, and metal-oxide is made of a semiconductor silicon layer covered (CMOS) with technology, a thinner an film IC isof alwayssilicon achieveddioxide (or from silica) a silicon in the wafer,first stage and of is manufacturing made of a silicon [18]. layer In spite covered of the with further a thinner technological film of siliconprocesses dioxide aimed (or silica)at deploying in the first the stage electronic of manufacturing circuitry [18 (e.g.,]. In spitedevices—like of the further transistors—and technological processesinterconnects) aimed onto at deploying the wafer, the the electronic on-chip circuitry wireless (e.g., channel devices—like is still often transistors—and represented as interconnects) the layered ontodielectric the wafer, structure the on-chip sketched wireless in Figure channel 2 [19]. is The still transmitter often represented (TX) and as thethe layeredreceiver dielectric (RX) are structureassumed sketchedburied inside in Figure the SiO2[ 192 layer]. The herein transmitter [11], but (TX) they and could thereceiver also lie on (RX) its are top assumed [9,10]. The buried upper inside medium the SiOabove2 layer SiO herein2 might [11 be], butair in they the could simplest also liecase on [10,11] its top or [9 ,10a different]. The upper passivation medium material above SiO (e.g.,2 might silicon be airnitride) in the [20]. simplest case [10,11] or a different passivation material (e.g., silicon nitride) [20].

Figure 2. On-chip radio channel as a layered medium. Figure 2. On-chip radio channel as a layered medium. It is worth mentioning that a pattern of some metallization layers is often inserted within the dielectricIt is regionworth mentioning [18], either forthat the a pattern interconnection of some metallization of the upper circuitlayers is elements often inserted or increasing within thethe reliabilitydielectric ofregion the manufacturing [18], either for process.the interconnectio The metallizationn of the canupper extend circuit over elem theents whole or chipincreasing area, i.e.,the itreliability is not necessarily of the manufacturing limited to the process. circuitry The regions. metallization Moreover, can extend a ground over plane the whole between chip the area, silicon i.e., substrateit is not necessarily and the insulating limited layerto the might circuitry be helpful regions. to preventMoreover, unwanted a ground electromagnetic plane between interference the silicon betweensubstrate the and antennas the insulating and the circuitry layer [might20]. be helpful to prevent unwanted electromagnetic interferenceFinally, thebetween presence the ofantennas the package and the housing circuitry of the [20]. IC can be also taken into account through the introductionFinally, ofthe further presence layers of respectivelythe package belowhousing and of abovethe IC the can silicon be also and taken the air/passivationinto account through slabs. Althoughthe introduction packages ofcan further be made layers of respectively several different below materials and above (e.g., the ceramic silicon or and plastic), the air/passivation the analysis is hereslabs. limited Although to the packages plastic case can for be the made sake of of several simplicity. different Since thematerials IC sometimes (e.g., ceramic lies on aor metal plastic), ground the actinganalysis as heatis here spreader limited [ 21to ],the the plastic bottom case layer for can the besake set of of simplicity. plastic or metal Since asthe a IC further sometimes option. lies on a metalIn ground summary, acting the as on-chip heat spreader wireless [21], channel the botto is herem layer sketched can be according set of plastic to the or following metal as a layered further structuresoption. (Figure3): In summary, the on-chip wireless channel is here sketched according to the following layered •structuresUnpacked (Figure, where 3): a plane silica slab including the transmitting and the receiving antennas is • boundedUnpacked by, where two different a plane media silica onslab the including upper and the on transmitting the lower side and (Figure the 3receivinga). The upper antennas region is canbounded be either by airtwo or different a different media passivation on the upper material, and where on the the lower former side case (Figure stands 3a). for The possible upper situationsregion can with be aeither refraction air or index a different in the superstrate passivation lower material, than inwhere the SiO the2. former The lower case zone stands can befor silicon or metal—in the latter case accounting for possible metallization layers inside the SiO2 or between the SiO2 and the Si regions. • Packed: where two additional layers are added at the bottom and on the top of the previous stack (Figure3b). Either plastic or metal can be considered for the bottom region, whereas plastic is the only option for the top half-space. J. Low Power Electron. Appl. 2018, 8, x FOR PEER REVIEW 5 of 16

possible situations with a refraction index in the superstrate lower than in the SiO2. The lower zone can be silicon or metal—in the latter case accounting for possible metallization layers inside the SiO2 or between the SiO2 and the Si regions. • Packed: where two additional layers are added at the bottom and on the top of the previous stack (Figure 3b). Either plastic or metal can be considered for the bottom region, whereas plastic is the only option for the top half-space. Each interface between different media is supposed perfectly flat and infinitely wide at this stage of the investigation, so that spatial wave propagation consists of multiple reflections occurring in the vertical plane (xz in Figure 3). The electromagnetic properties of the materials are taken into account through their refraction indexes (n coefficients in Figure 3), whose reference values in the optical range are listed in Table 1 together with the thickness considered for the different layers. Real values are assumed for the refraction indexes (i.e., the lossy materials have not been considered so J. Low Power Electron. Appl. 2018, 8, 39 5 of 16 far).

(a) (b)

Figure 3. Layered structures for the unpacked (a) and the packed ((b)) cases.cases.

Each interface betweenTable different 1. Major media input is parameters supposed for perfectly the RT simulator. flat and infinitely wide at this stage of the investigation, so that spatial wave propagation consists of multiple reflections occurring in the vertical plane (xz in FigureParameter3). The electromagnetic propertiesValue of the materials are taken into account through their refraction indexesΔh (n coefficientsthin: 6 μm; in medium: Figure3), 10 whose μm; referencethick: 14 μ valuesm in the optical range are listed in Table1 togetherΔh withup the thickness considered2 μm for the different layers. Real values are assumed for the refractionΔ indexeshdown (i.e., the lossy materials625 μm have not been considered so far). n0 1.44 (SiO2) Tablentop 1. Major input parameters1.5 (plastic) for the RT simulator. nup 1 (Air) or 2 (passivation) Parameter Value ndown 3.47 (Si, perfect metal otherwise) n∆bottomh 1.5 thin: (plastic, 6 µm; medium: perfect metal 10 µm; otherwise) thick: 14 µm ∆hup 2 µm ∆h 625 µm Although the proposeddown layouts are rather simplified compared to a real IC structure, they are n0 1.44 (SiO2) nonetheless expected to nfittop the need of providing1.5 a (plastic)reliable insight into the main properties of on-chip propagation, whichnup in the end is the primary1 (Air) or goal 2 (passivation) of this study. ndown 3.47 (Si, perfect metal otherwise) 4. Ray Tracing Propagationnbottom Modeling in1.5 OWiNoC (plastic, perfect metal otherwise) Channel modeling for OWiNoC can effectively rely on RT simulators, whose accuracy is known Although the proposed layouts are rather simplified compared to a real IC structure, they are to improve at large frequency as a general trend. nonetheless expected to fit the need of providing a reliable insight into the main properties of on-chip Furthermore, the description of the multi-core IC as a multi-layered structure with perfectly propagation, which in the end is the primary goal of this study. smooth, infinitely wide interfaces makes the ray tracing tasks easier, since the rays always lie in the 4. Ray Tracing Propagation Modeling in OWiNoC

Channel modeling for OWiNoC can effectively rely on RT simulators, whose accuracy is known to improve at large frequency as a general trend. Furthermore, the description of the multi-core IC as a multi-layered structure with perfectly smooth, inﬁnitely wide interfaces makes the ray tracing tasks easier, since the rays always lie in the same plane and the ﬁeld computation turns out to be simpler compared to a non-layered structure, as explained in the following sub-sections for the unpacked and packed cases, respectively. J. Low Power Electron. Appl. 2018, 8, x FOR PEER REVIEW 6 of 16

same plane and the field computation turns out to be simpler compared to a non-layered structure, J.as Low explained Power Electron. in the Appl. following2018, 8, 39 sub-sections for the unpacked and packed cases, respectively. 6 of 16

4.1. Unpacked Case 4.1. Unpacked Case Wave propagation consists of multiple reflections occurring within the SiO2 slab, as sketched in Wave propagation consists of multiple reflections occurring within the SiO slab, as sketched in Figure 4. Therefore, the electromagnetic field radiated to the RX after m bounces2 (m = 2 reflections Figure4. Therefore, the electromagnetic field radiated to the RX after m bounces (m = 2 reflections are are for instance shown in Figure 4a) can be expressed as: for instance shown in Figure4a) can be expressed as: −β   e jrm → =⋅→ −jβrm ⋅Π≥ EEm0me m ,m0 (2) E m = E 0m · r · Πm, m ≥ 0 (2) rmm

being β = 2π/λ the wave number, rm the overall length of the ray, Πm the product of the m reflection being β = 2π/λ the wave number, rm the overall length of the ray, Πm the product of the m reflection coefficients, and E0m the TX antenna “emitted field” in the direction of departure of the ray. It is coefficients, and E0m the TX antenna “emitted field” in the direction of departure of the ray. It is worth noting that Π0 = 1, since the direct ray undergoes no reflections. Moreover, the same reflection worth noting that Π0 = 1, since the direct ray undergoes no reflections. Moreover, the same reflection orderorderm m > > 0 0is is always always shared shared by by a couplea couple of raysof rays (as sketched(as sketched in Figure in Figure4a),the 4a), former the former having having the first the reflectionfirst reflection on the on upper the interfaceupper interface (and referred (and referred to as “up” to inas the “up” following), in the following), the latter on the the latter lower on one the (andlower identified one (and by identified the label by “down” the label herein). “down” herein).

(a) (b)

FigureFigure 4. 4.RT RT propagation propagation in in layered layered representation representation of of an an integrated integrated circuit: circuit: examples examples ofoptical of optical rays rays in thein the unpacked unpacked (a) and(a) and in the in packedthe packed (b) case.(b) case.

ItIt is is worth worth mentioning mentioning that that the the path path length length r mrmcan canbe be regarded regarded as as the the distance distance between between the the RX RX andand an an “mth“mth virtualvirtual transmitter”transmitter” (VTX), which is is the the ”mirror” “mirror” image image of of the the TX TX (if (if m m = =1) 1)or orof ofthe the (m (m− 1)th− 1)th VTXVTX (otherwise) (otherwise) with with respect respect to the to the reflecting reﬂecting plane plane (image (image principle) principle) [22]. [22 For]. For instance, instance, the theVTX VTX associated associated with with the the double double re reﬂectedflected “up-ray” “up-ray” is is included included in in FigureFigure4 a.4a. AccordingAccording to to the the consideredconsidered reference reference system, system, the the following following closed-form closed-form analytical analytical expressions expressions can can be be easily easily achieved achieved forfor the the VTXs VTXs locations locations in in the the unpacked unpacked case: case:

(  m,up m evenmeven:m : m · h⋅−() h− h h+ +z z z =m,up =  lowerlowerhigher higherTX TX (3) VTX zVTX  (3) m oddmodd:(m : (m + 1+⋅) 1)h· hhigher − −( (mm − −⋅ 1)h1) · hlower −− zzTX  higher lower TX ( m even : m · h − h + z m,down = meven:m⋅−+()higher hlower h zTX zVTX m,down =  higher lower TX (4) zVTX m odd : (m + 1) · h − (m − 1) · h − z (4) modd:() m+⋅ 1 hlower − () m −⋅ 1 hhigher − z TX  lower higher TX where zTX is the z-coordinate of the TX and hhigher and hlower are represented in Figures3 and4a. whereThe zTX evaluation is the z-coordinate of the Πm offactor the TX inEquation and hhigher (2) and requires hlower are the represented computation in of Figure the Fresnel 3 and reﬂectionFigure 4a. 2,up/down The evaluation of the Πm factor in Equation (2) requires the computation of the Fresnel coefﬁcients at the interfaces, and therefore of the angles of incidence of the rays (θinc in Figure4a). θ2,up/down reflection coefficients at the interfaces, and therefore of the angles of incidence of the rays ( inc

J. Low Power Electron. Appl. 2018, 8, 39 7 of 16

By means of simple geometrical considerations, the incidence angles can be related to the positions of both the RX and the VTX as follows:   m,up/down xRX θinc = arctg  (5) − m,up/down zRX zVTX

As a general rule, the larger the link distance (e.g., the xRX value) and/or the lower the number of undergone reflections, the “more grazing” the rays become, and therefore the greater the amount of reflected power. Since the reflection phenomenon also depends on the material properties (refraction index), the computation of Πm entails the assessment of the reflection coefficients at both the interfaces, which must be then properly multiplied taking into account the exact number of reflections occurring at the upper and at the lower boundaries. By definition, reflection coefficients always have an amplitude ≤1, meaning that depending on the materials and the incidence condition the power impinging on the upper and on the lower boundaries may be either constrained in the silica layer (total reflection) or leaked in the non-confined regions. Finally, the emitted field is computed as: v u m,up/down η θ →up/down u · PTX · gTX d t θm,up/down −jβ E 0m = · pˆ TX d · e (6) 2πn0 η π θm,up/down θm,up/down where = 120 , gTX( d ) and pˆ TX d are the transmitting antenna gain and polarization vector in the directions of departure of the up/down rays, respectively (as outlined in Figure4a). The following formulas can be exploited for the computation of Equation (6):

θm,up θm,up θm,down π θm,down d = inc , d = − inc (7)

Both the antenna gain pattern and the polarization vector in the propagation plane must be provided as input files to the RT engine; they may be indifferently achieved from numerical simulation of specific antenna layouts, or from simpler, ready-to-use analytical model representative of wider classes of antennas (e.g., isotropic, omnidirectional, directive, etc.). Since the Fresnel reflection coefficients are available only for the transverse electric (TE) and magnetic (TM) polarizations (corresponding respectively to the φˆ and θˆ directions in the considered reference system), the polarization vector and therefore the emitted field must be decomposed into its TE and TM components, and the corresponding field components should be then independently evaluated according to Equation (2). Once the rays have been tracked and the fields impinging on the RX have been computed, the overall received power can be achieved as [22]:

r r r 2 2 → Mrefl →up →down = λ · θ0 · θ0 · + θm,up · θm,up + θm,down · θm,down PRX 8πη gRX a pˆ RX a E 0 ∑ gRX a pˆ RX a E m gRX a pˆ RX a E m (8) m=1

→ 0 m,up/down being θa the direction of arrival at the RX of the direct field E 0, θa the angle of arrival at the RX of the up/down rays after n reflections, Mrefl the maximum number of allowed bounces, gRX and pˆ RX are the antenna gain and the polarization vector of the receiving antenna. The angle of arrival can be computed as: ( θm,up/down m,up/down d (m even) θa = (9) π θm,up/down − d (m odd) Since Equations (2)–(10) represent a set of rather simple, closed-form expressions, rays tracking turns out to be quite fast, with computation time of few minutes for simulations accounting for a J. Low Power Electron. Appl. 2018, 8, 39 8 of 16 number of reflections up to some hundreds. Commercial RT tools would hardly be as much effective, because they are not specifically conceived for multi-layer scenarios, and therefore they have to rely on more general but also computationally heavier ray tracing algorithms. Besides, full wave models (e.g., Finite-Difference Time-Domain methods (FDTD)) are not even worthy of consideration, since they simply cannot handle far-field analysis in inhomogeneous media. Finally, the resort to modal representation of the field seems also not appropriate, because in spite of the layered structures here considered, propagation is however wireless and therefore not necessarily confined in one guiding layer, as shown and discussed in Section5.

4.2. Packed Case If the materials bounding the silica slab also have finite thickness, additional rays rise within the layered structure, which can still undergo multiple reflections inside a layer but also propagate among the different layers exploiting transmission at the interfaces (Figure4b). Tracking such a huge multitude of rays would heavily increase the computational burden of the model, also because it would not simply consist of the closed-form, analytical formulas which hold in the Unpacked case. In order to trade off prediction accuracy against computational effort, propagation above and below the SiO2 layer in the packed case is here heuristically modeled by means of the “total layer reflection coefficient” proposed in Reference [23]. As a ray sprung from the TX impinges on the upper/lower interface, it is partly reflected and partly transmitted beyond the boundary, where it triggers a multiple bounce mechanism. Each time the bouncing ray hits back the silica slab, transmission takes place, spilling some field into the SiO2 layer. All these contributions add up coherently in such a way that the total field resulting from the multiple bounce phenomenon can be expressed through the following “enhanced” reflection coefficient to be applied directly to the impinging ray (see Reference [23] for details):

0 ∞ Γen = Γ + T · T · ∑ i=1(Ξi · ∆i · Λi · Σi) (10) where the involved coefﬁcients have the following meaning:

• Γ is the standard Fresnel reflection coefficient at the interface; • T and T0 are the outward and the inward transmission coefficients at the silica slab boundaries;

• Ξi is the product of the reﬂection coefﬁcients related to the rays bouncing in the upper/lower layer; • ∆i accounts for the phase shifts and propagation delays associated with the bouncing effect; • Λi and Σi take into account the attenuation experienced by the rays bouncing inside the layers, respectively associated with the possible material losses (actually not considered here, where lossless materials are supposed) and with the spatial spreading of the wavefronts. It is worth mentioning that Σi is actually not included in the original formula provided in Reference [23], and it has been here introduced to cope with the lack of respect for the plane wave and layer thinness conditions assumed in Reference [23].

In the end, propagation in the packed case can be modeled as for the unpacked case, provided that the Fresnel reﬂection coefﬁcients are replaced by the enhanced formulation.

5. Simulation Results and Discussion This section includes the outcomes of the RT model described in the previous section applied to the layered representations of the multi-core IC structure outlined in Section3.

5.1. RT Input Data In order to start the RT engine, the geometrical and electromagnetic description of both the propagation scenario (Table1) and the TX/RX antenna characteristics must be provided as input data. The simulation frequency is 193.5 THz, corresponding to a wavelength of 1.55 µm (in vacuum) and J. Low Power Electron. Appl. 2018, 8, x FOR PEER REVIEW 9 of 16 J. Low Power Electron. Appl. 2018, 8, 39 9 of 16 threshold of the incoming signal. The maximum reflection order is set to 300 reflections, both on upper and lower layers. thereforeAs far included as the in antennas the conventional radiation C-band properties for optical are concerned, telecommunications. either an Theisotropic emitted or powera simple by thedirective TX is 0pattern dBm and has the been RX supposed. sensitivity The has beendirective set to case−25 consists dBm, as of reasonable a simple detectionsingle-lobe threshold pattern ofalways the incoming steered in signal. the x Thedirection maximum (Figure reflection 4). In particular, order is setthe toradiation 300 reflections, intensity both is proportional on upper and to lowercosk(α layers.x), being αx < 90 deg. the angle between the direction of departure of the generic optical ray springingAs far out as thefrom antennas the Tx radiationantenna and properties the x axis. are concerned,The antenna either gain an G isotropic can be easily or a simple tuned directivethrough patternthe k coefficient, has been according supposed. to the The formula directive G case= 2∙(k consists + 1). Since of the a simple rays always single-lobe belong pattern to the vertical always k steeredplane, the in theRT simulator x direction must (Figure be actually4). In particular, fed by a thediscrete radiation representation intensity isof proportional the radiation to diagram cos (α xin), beingthe xzα plane,x < 90 as deg sketched. the angle in Figu betweenre 5 for the different direction G of values. departure The of pola therization generic opticalvector in ray the springing same plane out frommust thebe also Tx antenna provided, and in the orderx axis. to account The antenna for the gain polarimetric G can be easily properties tuned of through the antenna. the k coefficient, The same accordingantennas with to the TE formula polarization G = 2 ·(kare + assumed 1). Since at the the rays link always ends belongfor the tosake the of vertical simplicity, plane, pointing the RT simulatortoward each must other’s be actually (Figure fed 4). by a discrete representation of the radiation diagram in the xz plane, as sketchedAlthough in Figureanalytical5 for description different G of values. the antennas The polarization provides vectorextreme in flexibility, the same planesince mustas many be alsoradiation provided, patterns in order as necessary to account can for be the easily polarimetric achieved propertieswith negligible of the computation antenna. The effort, same any antennas other withradiation TE polarization pattern—e.g., are assumedbased on at thenumerical link ends simu forlation the sake of ofspecific simplicity, antenna pointing layout—can toward each be other’sinvestigated, (Figure provided4). that the required information is encoded in the correct format.

Figure 5. Examples of antenna radiation patterns resulting for different gain values. Figure 5. Examples of antenna radiation patterns resulting for different gain values. Although analytical description of the antennas provides extreme ﬂexibility, since as many radiationIn order patterns to distinguish as necessary the can different be easily possible achieved cases, with each negligible simulation computation is labeled effort,by means any otherof an radiationacronym pattern—e.g.,encoded as follows: based on numerical simulation of speciﬁc antenna layout—can be investigated, provided• Unpacked that the cases: required U_Δ informationstring_XY_GdB is encoded, where Δ instring the correct sets the format. width of the silica layer (possible Invalues: order “thin”, to distinguish “medium”, the “thick”, different see possible Table 1), cases, X and each Y are simulation characters is labeledidentifying by means the top of and an acronymthe down encoded media as follows: (X = “A”—Air—or “P”—Passivation -, and Y = “S”—Silicon—or “M”—Metal) • Unpackedand GdB is cases: the antennasU_∆string_XY_GdB gain value., whereFor instance,∆string the sets simulation the width ofcarried the silica out layerwith (possibleisotropic values:radiators “thin”, within “medium”, a 10 μm SiO “thick”,2 slab seebounded Table1 ),by X air and and Y are silicon characters at the upper identifying and lower the top interfaces and the downis referred media to (Xas =“U_medium_AS_0”; “A”—Air—or “P”—Passivation, and Y = “S”—Silicon—or “M”—Metal) and • GdBPacked is the cases: antennas P_Δstring_XYZ_GdB gain value. For, instance,where Δstring, the simulation X, Y and carriedGdB keep out their with meaning isotropic and radiators Z is a further character setting the material for the bottom layer (possible values: “P”—Plastic—or within a 10 µm SiO2 slab bounded by air and silicon at the upper and lower interfaces is referred to“M”—metal). as “U_medium_AS_0”; Therefore, adding a plastic package to the previous example would correspond to the label “P_medium_ASP_0”. • Packed cases: P_∆string_XYZ_GdB, where ∆string, X, Y and GdB keep their meaning and Z is a further character setting the material for the bottom layer (possible values: “P”—Plastic—or “M”—metal). Therefore, adding a plastic package to the previous example would correspond to the label “P_medium_ASP_0”.

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5.2.5.2. RTRT SimulationSimulation ResultsResults SeveralSeveral RT simulationssimulations havehave been been run run aiming aiming at theat the computation computation of the of link thePath link GainPath(PG) Gain under (PG) underdifferent different simulation simulation conditions. conditions. Path gain Path is gain deﬁned is defined as the ratioas the between ratio between the power the capturedpower captured by the byreceiving the receiving antenna antenna and the and power the power radiated radiated by the by transmitting the transmitting one [22one]. [22]. It therefore It therefore represents represents the thereciprocal reciprocal (the (the opposite, opposite, in dBin unit)dB unit) of the of the propagation propagation losses, losses, i.e., i.e., of the of the attenuation attenuation experienced experienced by bythe the optical optical wireless wireless signal signal as it as propagates it propagates from fr theom transmitting the transmitting to the to receiving the receiving antenna. antenna. Other lossesOther lossesmay further may further impair impair the communication the communication (e.g., coupling(e.g., coupling losses losses occurring occurring within within the circuits), the circuits), but they but theyarenot are considerednot considered in this in study.this study. PGPG is is plotted plotted versus versus the the link link distance distance (μ (m)µm) in inFigure Figure 6,6 for, for different different materials materials combinations combinations in inthe unpackedthe unpacked case caseand assuming and assuming isotropic isotropic radiators. radiators. The TX The and TX the and RX the are RX placed are placed in the inmiddle the middle of the of the SiO slab with medium thickness. The free space power is also drawn (black straight line), SiO2 slab with2 medium thickness. The free space power is also drawn (black straight line), as reference.as reference. Two Two “breakpoints” “breakpoints” cancan be highlighted be highlighted as a as general a general trend, trend, the theformer former corresponding corresponding to the to the distance where the PG rises up from the free-space line (rise point—P ), the latter representing the distance where the PG rises up from the free-space line (rise point—Prr), the latter representing the farther distance where the PG drops below the free space curve (fall point—P ). Three zones can be farther distance where the PG drops below the free space curve (fall point—Pff). Three zones can be identifiedidentiﬁed accordingly: accordingly:

•• FreeFree SpaceSpace ZoneZone:: beforebefore PPrr TXTX andand RXRX areare quitequite closeclose eacheach otherother andand propagationpropagation isis dominateddominated byby thethe directdirect path,path, sincesince thethe reflectedreflected raysrays areare muchmuch longerlonger (in(in relativerelative terms)terms) andand undergoundergo almostalmost normalnormal incidence incidence at at the the interfaces, interfaces, which which corresponds correspon tods theto the greatest greatest reflection reflection loss. loss. Although Although this zonethis zone is quite is quite limited limited to the to near the fieldnear regionfield region in the in isotropic the isotropic case, wherecase, where RT accuracy RT accuracy is likely is tolikely be poor, to be it neverthelesspoor, it nevertheless extends intoextends the far-fieldinto the region far-field for region increasing for antennaincreasing directivity antenna (asdirectivity explained (as in explained the following in the Figure following6); Figure 6); •• PremiumPremium Zone Zone:: a a noticeable noticeable power power gain gain occurs occurs between between Pr and Pr and Pf compared Pf compared to the to free the spacefree space case, likelycase, duelikely to due a sort to of a guiding sort of effect,guiding which effect, sets which up within sets theup silicawithin layer. the Multipathsilica layer. composition Multipath iscomposition constructive is onconstructive average, and on firstaverage, triggers and oscillations first triggers of oscillations the PG, finding of the then PG, a finding regular then slope a withregular no fadesslope inwith most no of fades the cases in most represented of the cases in Figure represented6. The spatialin Figure average 6. The of spatial the PG average decay in of thisthe zonePG decay as 1/d inα this, α

FigureFigure 6.6.Path Path gain gain vs. vs. TX-RX TX-RX distance distance in thein the unpacked unpacked case case with with medium medium thickness thickness of the of silica the layer,silica differentlayer, different substrate substrate and superstrate, and superstrate, and assuming and assumi isotropicng isotropic radiators. radiators.

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As clearly shown in Figure6 6,, thisthis generalgeneral analysisanalysis doesdoes notnot fullyfully explainexplain thethe U_medium_AM_0U_medium_AM_0 case, where the the super- super- and and the the substrate substrate are are ma madede of of air air and and metal, metal, respectively. respectively. Since Since nupn

Figure 7. Pr and Pf distances vs. TX/RX antenna gain. Unpacked case with medium thickness of the Figure 7. Pr and Pf distances vs. TX/RX antenna gain. Unpacked case with medium thickness of the silica slab and silicon underneath.

This behavior may be explained by the impact of the antennas radiation pattern on the intensity of the multipath contributions. As a matter of fact, increasing the directivity boosts the amplitude of the direct path, to the detriment of the reﬂectedreflected ones.ones. Therefore, the widening of the free-space zone (corresponding to the larger Prr value) for increasing gain is not surprising, since it exactly represents the distancedistance rangerange wherewhere propagation propagation is is primarily primarily ruled ruled by by the the direct direct ray. ray. Furthermore, Furthermore, the the larger larger the directivity,the directivity, the poorer the poorer the power the power gain attained gain attain overed the over free spacethe free reference space case,reference because case, weakening because theweakening intensity the of theintensity reﬂected of the rays reflected impairs therays multipath impairs the constructive multipath interference constructive the interference guiding effect the reliesguiding on. effect This leadsrelies toon. the This progressive leads to reductionthe progressive of Pf at reduction large G values. of Pf at In large summary, G values. the more In summary, directive the antennas,more directive the stronger the antennas, the signal the stronger intensity the conveyed signal intensity at the RX conveyed by the direct at the ray, RX thus by the dumping direct multipathray, thus dumping fading, but multipath the lower fading, the further but receivedthe lowe powerr the further adding upreceived in the premiumpower adding zone becauseup in the of thepremium guiding zone effect. because Therefore, of the the guiding optimal effect. gain valueTheref shouldore, the trade optimal off the gain two value aspects should against trade each off other. the two aspectsFigure8 against shows theeach sensitivity other. of the breakpoints to both the antennas placement within the silica layerFigure and its 8 thickness.shows the It sensitivity is clear that of thethe thicknessbreakpoints represents to both athe crucial antennas element, placement since P withinf increases the fromsilica aboutlayer 1mmand its to thickness. nearly 20mm It is moving clear that from th thee thickness thin to the represents thick case. a Acrucial similar element, trend holds since forPf Pincreasesr, although from to about a lesser 1mm extent. to nearly In contrast, 20mm moving opposite fr effectsom the arethin triggered to the thick by shiftingcase. A similar the antennas trend withinholds for the P slab,r, although with P rtoclearly a lesser increasing extent. andIn contrast, instead Poppositef slightly effects decreasing are triggered as the TX/RX by shifting approach the theantennas upward/downward within the slab, boundaries.with Pr clearly Therefore, increasing the and thicker instead the silicaPf slightly layer, decreasi the widerng theas the premium TX/RX zone,approach whereas the upward/downward the closer the antennas boun todaries. the interfaces, Therefore, the the shorter thicker it becomes. the silica layer, the wider the premium zone, whereas the closer the antennas to the interfaces, the shorter it becomes. Although the results in Figure 8 refer to the unpacked case with passivation material and silicon respectively filling the super- and the substrate, the highlighted trends still hold in the other cases.

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The package impact on the wireless channel characteristics is investigated in Figure 9, where the PG is plotted against the link distance with (continuous lines) and without (dotted lines) package. It can be first noted that the general trends previously highlighted in the unpacked case still hold when the package is also taken into account, since the two breakpoints and the corresponding three zones can be again identified after all. Moreover, larger Pf values are still detected when the J. Low Power Electron. Appl. 2018, 8, 39 12 of 16 superstrate is made of air, likely because the total reflection effect occurs at the SiO2-Air interface regardless of the upper layers.

J. Low Power Electron. Appl. 2018, 8, x FOR PEER REVIEW 12 of 16

The package impact on the wireless channel characteristics is investigated in Figure 9, where the PG is plotted against the link distance with (continuous lines) and without (dotted lines) package. It can be first noted that the general trends previously highlighted in the unpacked case still hold when the package is also taken into account, since the two breakpoints and the corresponding three zones can be again identified after all. Moreover, larger Pf values are still detected when the superstrate is made of air, likely because the total reflection effect occurs at the SiO2-Air interface regardless of the upper layers.

(a) (b)

FigureFigure 8. 8. SensitivitySensitivity of the the rise rise (a ()a )and and the the fall fall (b) (pointsb) points to the to silica the silica slab thickness slab thickness and the and antenna the antennaplacement. placement. Isotropic, Isotropic, unpacked unpacked case with case passivatio with passivationn and silicon and filling silicon the super- ﬁlling and the the super- substrate, and therespectively. substrate, respectively.

Although the results in Figure8 refer to the unpacked case with passivation material and silicon respectively filling the super- and the substrate, the highlighted trends still hold in the other cases. The package impact on the wireless channel characteristics is investigated in Figure9, where the PG is plotted against the link distance with (continuous lines) and without (dotted lines) package. It can be first noted that the(a) general trends previously highlighted in the unpacked(b) case still hold when the package is also taken into account, since the two breakpoints and the corresponding three zones Figure 8. Sensitivity of the rise (a) and the fall (b) points to the silica slab thickness and the antenna can be again identified after all. Moreover, larger Pf values are still detected when the superstrate is placement. Isotropic, unpacked case with passivation and silicon filling the super- and the substrate, made of air, likely because the total reflection effect occurs at the SiO2-Air interface regardless of the respectively. upper layers. (a) (b)

Figure 9. Comparison between unpacked and packed arrangements, for medium thickness of the silica layer and isotropic radiators. The superstrate is filled with air (a) or with a passivation material (b).

The introduction of the package is fundamentally transparent as far as propagation issues are concerned if the unpacked die behaves as a full guiding structure (U_medium_AM_0 basically coincident with P_medium_AMM_0 in Figure 9a). In the other cases, a plastic package seems to affect the total PG to a lesser extent than it does when (partly) made of metal, because the presence of metal underneath the( asilicon) bulk can enable total reflection mechanisms(b) which are not triggered otherwise. Similarly, the presence of a plastic layer on the top of the layered stack more significantly FigureFigure 9.9.Comparison Comparison between between unpacked unpacked and and packed packed arrangements, arrangements, for mediumfor medium thickness thickness of the of silica the affects the RT outcomes when the layer underneath is filled with the passivation material, since it layersilica andlayer isotropic and isotropic radiators. radiators. The superstrate The superstrate is filled is withfilled air with (a) air or with(a) or a with passivation a passivation material material (b). restores the conditions for total reflection at the plastic-passivation interface, which are not fulfilled (b). at theThe SiO introduction2-passivation of boundary. the package is fundamentally transparent as far as propagation issues are concernedTheIn introduction ifsummary, the unpacked theof the package diepackage behaves seems is fundamentally as more a full importan guiding transparentt structureevery timeas(U_medium_AM_0 far itsas propagationpresence enforces issues basically totalare coincidentconcernedreflection withphenomenaif the P_medium_AMM_0 unpacked not occurring die behaves inat the Figure as inner a 9fulla). interfaces. guiding In the other structure cases, (U_medium_AM_0 a plastic package seems basically to affectcoincident theThe total maximumwith PG P_medium_AMM_0 to acommunication lesser extent than rangein itFigure does (dmax when9a).) is evaluatedIn (partly) the other madein Figurecases, of metal, a10 pl forasticbecause different package the antenna presenceseems gain to ofaffectand metal packedthe underneath total layouts. PG to thea lesserIn silicon this extent study, bulk than candmax it enablesimply does when total corresponds reflection(partly) madeto mechanisms the of link metal, distance which because where are the not presencethe triggered received of otherwise.metalpower underneath equals Similarly, the the RX the siliconsensitivity presence bulk of(here can a plastic enable set to layer −tota25 onldBm, reflection the Table top of mechanisms 1) the after layered the signal stackwhich more fluctuationsare not significantly triggered due to affectsotherwise.multipath the RTSimilarly, fading outcomes have the whenpresencebeen spatially the of layer a plastic averaged. underneath layer Compared on is the filled top with ofto the the layeredreference passivation stack free more material,space significantly case, since where it restoresaffects the the RT conditions outcomes for when total reflectionthe layer atunderneath the plastic-passivation is filled with interface, the passivation which are material, not fulfilled since at it therestores SiO2-passivation the conditions boundary. for total reflection at the plastic-passivation interface, which are not fulfilled at theIn SiO summary,2-passivation the package boundary. seems more important every time its presence enforces total reflection phenomenaIn summary, not occurring the package at the inner seems interfaces. more important every time its presence enforces total reflection phenomena not occurring at the inner interfaces. The maximum communication range (dmax) is evaluated in Figure 10 for different antenna gain and packed layouts. In this study, dmax simply corresponds to the link distance where the received power equals the RX sensitivity (here set to −25 dBm, Table 1) after the signal fluctuations due to multipath fading have been spatially averaged. Compared to the reference free space case, where

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The maximum communication range (dmax) is evaluated in Figure 10 for different antenna gain and packed layouts. In this study, dmax simply corresponds to the link distance where the received power equals the RX sensitivity (here set to −25 dBm, Table1) after the signal fluctuations due to multipathJ. Low Power fading Electron. have Appl. been 2018, spatially8, x FOR PEER averaged. REVIEW Compared to the reference free space case, whered 13max of 16 linearly increases with G, the layered structures behave rather differently. If the gain is too low, ad largemax linearly amount increases of power with is G, lost the because layered of structures the large be refractionhave rather losses differently. undergone If the by gain the is rays too farlow, froma large total amount reflection of power conditions is lost inbecause most cases.of the large Increasing refraction the antennalosses undergone gain is therefore by the rays beneficial far from andtotal the reflection curve rises conditions up to a peak,in most clearly cases. visible Increasi inng Figure the antenna 10a. Thereafter gain is therefore the trend beneficial is reversed and and the dmaxcurvestarts rises decreasing up to a peak, as Gclearly keeps visible on increasing. in Figure 10a. As alreadyThereafter discussed, the trend the is reversed guiding and effect dmax taking starts placedecreasing in the premium as G keeps zone on is increasing. impaired by As excessive already directivitydiscussed, levels.the guiding As the effect premium taking zone place shrinks in the back,premium the communication zone is impaired range by steadilyexcessive drops directivity towards levels. the freeAs the space premium situation, zone that shrinks is attained back, asthe sooncommunication as the premium range zone steadily disappears drops to (Pwardsr = P fthe). Then, free space propagation situation, conditions that is attained are always as soon worse as the thanpremium free-space zone as disappears far as the d(Pmaxr = Pvaluef). Then, is concerned. propagation Therefore, conditions very are large always gain worse values than are free-space not only useless,as far as but the even dmax harmful,value is concerned. and the optimal Therefore, directivity very large corresponds gain values to the are peaknot only of the useless, link distance but even curve.harmful, Although and the the optimal peak directivity position is corresponds affected by theto th silicae peak layer of the thickness link distance (Figure curve. 10a) Although and by the the differentpeak position material is combinationsaffected by the (Figure silica 10 layerb), the thic outlinedkness (Figure general analysis10a) and holds by the for different the whole material set of consideredcombinations cases. (Figure 10b), the outlined general analysis holds for the whole set of considered cases.

(a) (b)

FigureFigure 10. 10.Link Link distance distance vs. antennavs. antenna gain gain for the for packed the packed scenario scenario and middle and placedmiddle TX/RX.placed (TX/RX.a) Plastic (a) package,Plastic package, up-layer passivation,up-layer pass differentivation, thicknessdifferent thickness (b) comparison (b) comparison between differentbetween packeddifferent layouts, packed mediumlayouts, thickness. medium thickness.

AsAs long long as as the the guiding guiding mechanism mechanism can can be be relied relied on, on, dmax dmax= = 1 1 mm mm can can be be achieved achieved with with G G equal equal to to aboutabout 20 20 dB, dB, that that is is approximately approximately 10 10 dB dB less less than than the the free free space space requirement. requirement.

5.3.5.3. Preliminary Preliminary Validation Validation of of Results Results AsAs geometrical geometrical optics optics isis anan asymptotic theory, reliable reliable predictions predictions should should be be expected expected when when RT RTis isrun run at atoptical optical frequencies. frequencies. Neve Nevertheless,rtheless, several several factors factors might might impa impairir the theRT RTactual actual accuracy, accuracy, e.g., e.g.,related related to surface to surface propagation propagation phenomena phenomena and/or and/or near-field near-field coupling coupling effects, effects, which which has hasnot notbeen beentaken taken into into account account by bythe the ray ray approach. approach. Furt Furtherher numerical approximationsapproximations maymay comecome from from unavoidableunavoidable interpolation interpolation of the of antenna the antenna radiation diagram,radiation asdiagram, the rays directionas the of rays departure/arrival direction of dodeparture/arrival not exactly coincide do not with exactly the samples coincide stored with inthe the samples corresponding stored in input the corresponding file. input file. BecauseBecause of of the the many many difficulties difficulties in in carrying carrying out ou on-chipt on-chip wireless wireless measurements measurements in in the the optical optical bands,bands, experimental experimental data data to to compare compare with with the the RT RT simulations simulations are are currently currently not not available. available. Therefore, Therefore, RTRT predictions predictions have have been been checked checked against against a a full-wave, full-wave, FDTD FDTD simulator simulator in in the the unpacked unpacked case case and and for for somesome different different thickness thickness of theof layers.the layers. Since Since the full-wave the full-wave simulation simulation requires requires a specific a antennaspecific layout,antenna results in Figure 11 compare the field distribution generated along the axis of the SiO layer by the layout, results in Figure 11 compare the field distribution generated along the axis of2 the SiO2 layer µ opticalby the antenna optical describedantenna described in Reference in Reference [8]. The distance [8]. The rangedistance is limited range is to limited about 100 to aboutm to 100 keep μ them to computationalkeep the computational burden affecting burden FDTD affecting simulation FDTD simulation under control. under control. The overall mean error and error standard deviation amount to −0.7 dB and 2.2 dB, respectively. Overall, the agreement is quite satisfactory, given that RT accuracy for path-loss modeling in outdoor, cellular systems usually correspond to a prediction error standard deviation of several dBs even in the best cases. Anyway, further and deeper investigations are needed to fully assess the reliability of the proposed RT approach for on-chip propagation modeling.

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(a) (b)

FigureFigure 11. 11.Comparison Comparison between between RT RT and and FDTD FDTD prediction prediction of the of ﬁeldthe field distribution distribution along along the axis the ofaxis the of silicathe silica layer. layer. Thickness Thickness of the of silica the silica layer layer equal equal to 3.5 toµm 3.5 (a μ)m and (a) 4 andµm (4b μ).m (b).

6. ConclusionsThe overall mean error and error standard deviation amount to −0.7 dB and 2.2 dB, respectively. Overall, the agreement is quite satisfactory, given that RT accuracy for path-loss modeling in outdoor, Optical wireless networks on-chip can provide effective interconnection of cores in chip cellular systems usually correspond to a prediction error standard deviation of several dBs even in the multiprocessor in terms of latency, layout complexity, and antenna integration. Nevertheless, best cases. inter-core communications might be thwarted by propagation losses (particularly heavy in the Anyway, further and deeper investigations are needed to fully assess the reliability of the proposed optical range) and/or by possible multipath effects. Characterizing the wireless channel is therefore RT approach for on-chip propagation modeling. important to predict the actual reliability of the communications and/or to design technical solutions 6.to Conclusions increase the system robustness to propagation impairments. Investigations on the main properties of on-chip wireless optical propagation have been carried out in this work through a ray tracing Optical wireless networks on-chip can provide effective interconnection of cores in chip approach applied to a layered representation of the chip structure, with the transmitter and the multiprocessor in terms of latency, layout complexity, and antenna integration. Nevertheless, inter-core receiver included in the same silica layer. communications might be thwarted by propagation losses (particularly heavy in the optical range) Results have highlighted the presence of three major spatial regions, namely free-space, and/or by possible multipath effects. Characterizing the wireless channel is therefore important to premium, and fall zone, with different path-loss characteristics. At short distance, multipath is predict the actual reliability of the communications and/or to design technical solutions to increase primarily ruled by the direct path, and the spatial average of the received power decays with the system robustness to propagation impairments. Investigations on the main properties of on-chip distance as in free space. Then, the reflected rays become stronger and interfere constructively, thus wireless optical propagation have been carried out in this work through a ray tracing approach applied triggering some kind of guiding effect, which results in a power gain with respect to free space. to a layered representation of the chip structure, with the transmitter and the receiver included in the Finally, multipath interference turns round, and the received power decreases with distance at a rate same silica layer. steeper than free space. The size of the premium zone depends on several factors, like the antenna Results have highlighted the presence of three major spatial regions, namely free-space, premium, directivity, and position, the thickness of the layers and the materials they are made of. As a general and fall zone, with different path-loss characteristics. At short distance, multipath is primarily ruled trend, it extends for thicker silica layer, whereas it shrinks as the antennas approach the layer by the direct path, and the spatial average of the received power decays with distance as in free space. boundaries or become more directive. As a consequence, the communication range peaks at the Then, the reflected rays become stronger and interfere constructively, thus triggering some kind of antenna gain value corresponding to the optimal trade-off between the power directly conveyed at guidingthe receiver effect, by which the direct results path in a and power the gainadditional with respect extra-power to free carried space. Finally, by the guided multipath reflected interference paths. turns round,The presence and the of received a package power around decreases the die with affects distance the at propagation a rate steeper characteristics than free space. to Thea limited size ofextent, the premium and it seems zone depends more important on several every factors, time like its the presence antenna enforces directivity, total and reflection position, phenomena the thickness not ofoccurring the layers otherwise. and the materials they are made of. As a general trend, it extends for thicker silica layer, whereasFinally, it shrinks it is worth as the highlighting antennas approach that the thedevel layeropment boundaries of reliable or propagation become more models directive. represents As a consequence,a basic, valuable the communication asset for the effective range peaks design at of the the antenna whole gain network value on corresponding chip, e.g., it may to the enable optimal the trade-offassessment between of interference the power directlyissues always conveyed arising at the in receiver presence by of the multiple direct path wireless and the links. additional In fact, extra-powerpropagation carried awareness by the is guided ultimately reflected necessary paths. to estimate the signal-to-interference ratios, which are Thealways presence somehow of a related package to aroundthe overall the perfor die affectsmance the of propagationthe wireless communication characteristics tosystem. a limited extent, and it seems more important every time its presence enforces total reflection phenomena not occurringAuthor Contributions: otherwise. Conceptualization: F.F., M.B., and G.B.; Methodology: F.F., M.B., and G.B.; Software: F.F.,Finally, M.B., and it is worthM.Z.; Validation: highlighting F.F., that M.B., the and development M.Z.; Data of Curation: reliable propagationF.F., M.B., M.Z., models G.B., represents and G.C.; aWriting—Original basic, valuable assetDraft forPreparation: the effective F.F., M.B., design and of M.Z.; the wholeWriting—Review network on& Editing: chip, e.g.,F.F., itM.B., may M.Z., enable G.B., theG.C., assessment P.B., and V.P.; of interference Supervision: issuesF.F., P.B., always and V.P. arising in presence of multiple wireless links. In fact, propagationFunding: This awareness research was is ultimately funded by the necessary Italian Ministry to estimate of Education, the signal-to-interference University and Research ratios, (MIUR) which in are the alwaysframework somehow of the related PRIN 2015 to the “Wireless overall performanceNetworks through of the on-chip wireless Optical communication Technology—WiNOT” system. Project (20155EA8BC-PE7).

Conflicts of Interest: The authors declare no conflict of interest.

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Author Contributions: Conceptualization: F.F., M.B., and G.B.; Methodology: F.F., M.B., and G.B.; Software: F.F., M.B., and M.Z.; Validation: F.F., M.B., and M.Z.; Data Curation: F.F., M.B., M.Z., G.B., and G.C.; Writing—Original Draft Preparation: F.F., M.B., and M.Z.; Writing—Review & Editing: F.F., M.B., M.Z., G.B., G.C., P.B., and V.P.; Supervision: F.F., P.B., and V.P. Funding: This research was funded by the Italian Ministry of Education, University and Research (MIUR) in the framework of the PRIN 2015 “Wireless Networks through on-chip Optical Technology—WiNOT” Project (20155EA8BC-PE7). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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