Patent Description:
Silicon-based PICs benefit from low optical losses, ease of integration with electronic components, and manufacturability using standard photolithographic techniques. To allow for the integration of active photonic devices - such as lasers, optical amplifiers, optical modulators, and photodetectors - into the photonic circuits, III-V materials, which feature high electro-optic efficiency, may be combined with silicon in a heterogeneous (sometimes also referred to as "hybrid") material platform. A common way of achieving such heterogeneous material integration involves bonding III-V die to a pre-patterned silicon-on-insulator (SOI) wafer, and coupling light between a silicon waveguide in the wafer and the optically active III-V region. In some applications, the light couples evanescently from the silicon waveguide to the active region, but this approach provides only limited overlap between the optical mode and the active region, as a large portion of the optical mode remains guided in the silicon waveguide. To maximize the overlap with the active region, therefore, many applications use tapered waveguide transitions between silicon and III-V waveguides to fully transfer the optical mode to the III-V waveguide and/or back to the silicon waveguide.

The performance of a laser or other active device utilizing a tapered waveguide transitions depends in no small part on the optical losses that the guided light incurs along the waveguide due to scattering into undesired higher-order modes. In general, scattering losses can be reduced by making the change in width more gradual, and thus the taper longer. However, longer tapers come with their own problems. In single-mode laser applications, for instance, the laser cavity, which includes the waveguide taper, is preferably made as short as possible to make single-mode operation easier. Also, light propagation losses in the bulk of the waveguide increase linearly with length. Accordingly, a low-loss, yet compact waveguide transition is desirable.

<CIT> makes reference to an asymmetric twin waveguide (ATG) structure with quantum- well intermixing in the taper region of the active waveguide. The structure comprises a first waveguide, a second waveguide, and a taper formed in the second waveguide. The taper has an intermixed area formed therein comprising a plurality of quantum wells intermixed with a plurality of barriers. The quantum wells and barriers may be intermixed using plasma-enhanced intermixing such as, for example, Argon plasma enhanced intermixing. Quantum- well intermixing reduces absorption loss normally encountered in the movement of light between waveguides. <NPL>, refers to a waveguide transition comprising a tapered section. With reference to claim <NUM>, these documents do not disclose, at least, computing a scattering rate as a function of waveguide width of the waveguide taper for each of the multiple sets of parameter values; determining an envelope of the scattering rates for the multiple sets of parameter values, wherein the envelope is a curve that provides an upper bound to all process cases collectively by determining, at each waveguide width, the maximum scattering rate across all process comers and linearly interpolating between local maxima across waveguide width; computing a non-linear taper profile of the waveguide taper based on the envelope; and fabricating the waveguide transition based on the computed non-linear taper profile.

In the following description of embodiments of the disclosed subject matter, reference is made to the accompanying drawings.

Described herein is an approach to designing optical waveguide transitions with one or more non-linear waveguide tapers that optimizes the trade-off between taper length and scattering losses. In non-linear waveguide tapers, the taper profile, herein understood as the change in waveguide width as a function of length along the waveguide taper, is non-linear. For a given change in waveguide width over a given taper length, suitable non-linear waveguide taper profiles can achieve lower losses than linear waveguide taper profiles; or, conversely, for a given limit on acceptable scattering losses, non-linear waveguide tapers can be designed shorter.

The precise taper profile that achieves optimal performance depends on the scattering rate as a function of waveguide width. The width-dependent scattering rate, in turn, depends on design parameters of the waveguide transition, such as the fabricated dimensions (e.g., layer thicknesses) and material properties (e.g., the refractive index) of the waveguide transition. Those parameters, however, are in practice subject to process variations in fabrication. Dimensional parameters prone to fabrication variation include, e.g., etch depths, alignments, and widths of lithographic process layers and material thicknesses. Further, the refractive index, which is generally defined by the materials used, may be subject to fabrication variations due to variations in material stoichiometry or stresses. A waveguide transition manufactured according to a taper profile computed based on the nominal design parameters, therefore, generally falls short of the theoretical performance. Rather than simply "stretching" the waveguide taper to compensate for any variations in the design parameters and keep the scattering losses associated with the waveguide transition below a specified acceptable limit, the proposed design approach takes the process variations into account to generate a fabrication-tolerant non-linear taper profile optimized jointly for multiple combinations of variations in the design parameters. According to the claimed invention, the expected range of variations is captured in multiple sets of parameter values of the design parameters, including a set of nominal parameter values and sets of parameter values representing the most extreme variations in design parameters that are still within acceptable margins, i.e., result in devices that still pass quality inspection (rather than being discarded); these process variation extremes are commonly referred to as "process corners.

According to the claimed invention, designing a fabrication-tolerant waveguide taper profile involves computing the width-dependent scattering rate for multiple sets of values of the design parameters for the nominal parameter values and sets of parameters values associated with the process corners, and determining the envelope of the computed scattering rates, which represents the worst-case scattering rate for each width along the taper. The non-linear taper profile is then calculated based on the envelope. The taper profile can be straightforwardly scaled to any taper length. In some embodiments, scattering losses along the waveguide taper are simulated based on the computed taper profile for a specified taper length and for the multiple sets of design parameter values to determine an associated range of optical transmission values for the waveguide transition, the minimum transmission of the range representing the achievable performance of the waveguide transition. Further, the simulation may be performed for multiple values of the taper length (e.g., corresponding to a discretized range of lengths) to determine, for a specified threshold transmission value, how long the taper should be to exceed the threshold transmission value for all of the simulated sets of design parameter values. Once the taper profile and taper length have been determined, the waveguide transition can be fabricated in accordance with that profile, e.g., by patterning the semiconductor device layer of a substrate to form the bottom one of the two waveguides, depositing another layer of material (e.g., a III-V semiconductor material as may be used in active photonic devices) above the bottom waveguide, and patterning that top layer to form the top waveguide of the transition. The taper may be included in either one of the bottom waveguide or the top waveguide. Further, in some embodiments, both waveguides are tapered in an overlapping fashion, with profiles computed based on the envelope of scattering rates for multiple sets of design parameter values.

The foregoing will be more readily understood from the following description of the accompanying drawings, which illustrate various example embodiments and underlying principles.

<FIG> and <FIG> are top and side views, respectively, of an example heterogeneous photonic structure <NUM> including waveguide transitions with a tapered bottom waveguide <NUM>, which are helpful to understand the invention. <FIG> are cross-sectional views of the heterogeneous tapered waveguide transitions of <FIG> and <FIG> at two locations along the waveguide length. The waveguide transitions are formed between the tapered bottom waveguide <NUM> created in (e.g., a device layer <NUM> of) a substrate <NUM>, and a top waveguide <NUM> formed above the substrate <NUM>. The bottom and top waveguides <NUM>, <NUM> may generally be made from any combination of light-guiding material, including semiconductor materials (such as silicon or III-V compound semiconductor material) or dielectrics. For example, the waveguide transition may include a III-V material (for the top waveguide <NUM>) on silicon (for the bottom waveguide <NUM>), a dielectric on silicon, a III-V material on a dielectric, a dielectric on another dielectric, etc..

In some embodiments, as can be seen in <FIG>, the substrate <NUM> is an SOI or other semiconductor-on-insulator substrate including a handle layer <NUM> (e.g., of silicon, diamond), a buried oxide (BOX) or other insulating layer <NUM> on top of the handle layer <NUM>, and the semiconductor device layer <NUM> (e.g., made of silicon) on top of the insulating layer <NUM>. The top waveguide <NUM> may be bonded directly to the semiconductor device layer <NUM>, as shown, or to an optional thin bonding layer (e.g., made of silica) deposited above the semiconductor device layer <NUM>. As shown, the top waveguide <NUM> may include multiple layers, including an optically active layer <NUM>, where light can be generated or absorbed. In various embodiments, the top waveguide <NUM> is made of one or more III-V materials (such as, e.g., indium phosphide (InP), indium arsenide (InAs), gallium arsenide (GaAs), gallium nitride (GaN), or indium antimonide (InSb)), or alternatively of II-VI compound semiconductor materials.

The bottom waveguide <NUM> may be defined in the device layer <NUM> by channels <NUM> etched into the device layer <NUM>. For a rib waveguide, as shown in <FIG> and1D, the device layer <NUM> is etched only partially, leaving a thin slab <NUM> of material (e.g., silicon), on which the rib rests. Light coupled into the bottom waveguide <NUM> at one end generally propagates along the bottom waveguide <NUM> to the other end, as indicated by arrows <NUM> in <FIG>. In a region in which the bottom and top waveguides <NUM>, <NUM> overlap, the light couples at least partially from the bottom waveguide <NUM> up into the top waveguide <NUM> in a first waveguide transition, propagates to the other end of the top waveguide <NUM>, and couples back down into the bottom waveguide <NUM> in a second waveguide transition, as shown by arrows <NUM> in <FIG>. To facilitate good optical coupling, the bottom waveguide <NUM> gradually decreases in width in the first waveguide transition at the start of the overlap region, forming a waveguide taper <NUM>. In the second waveguide transition at the end of the overlap region, the bottom waveguide <NUM> tapers back up, e.g., to its original width, along a second waveguide taper <NUM>, which may be mirror-symmetric to the first taper <NUM>. <FIG> depicts the cross section at the beginning of the overlap region between the two waveguides <NUM>, <NUM>, where the bottom waveguide still has its maximum width. (The same cross section applies to the end of the overlap region, following the taper <NUM>. ) <FIG> shows a cross section near the tip of the taper <NUM> (or, similarly, near the tip of the taper <NUM>). In between the tips (understood to be the narrowest ends) of the tapers <NUM>, <NUM>, the bottom waveguide <NUM> may persist as a narrow waveguide (e.g., of a small constant width), as shown, and some of the optical power may remain and be carried in that narrow strip of the bottom waveguide <NUM>. Alternatively, the bottom waveguide <NUM> may taper all the way down to a point in each taper <NUM>, <NUM>, vanishing in between the tapers <NUM>, <NUM>.

<FIG> and <FIG> are top and side views, respectively, of an example heterogeneous photonic structure <NUM> including waveguide transitions with a tapered top waveguide <NUM>, fabricated in accordance with the claimed method. <FIG> are cross-sectional views of the heterogeneous photonic structure <NUM> of <FIG> and <FIG> at two locations along the tapered waveguide transitions. The bottom waveguide <NUM> has, in this example, constant width along the overlap region between the waveguides <NUM>, <NUM>. The top waveguide <NUM> includes a center region <NUM> of constant width, preceded and followed by waveguide tapers <NUM>, <NUM>. In a first waveguide transition at the start of the overlap region between the two waveguides <NUM>, <NUM>, where the waveguide <NUM> tapers up, light is coupled from the bottom waveguide into the top waveguide <NUM>, as shown by arrows <NUM> in <FIG>. In the center region <NUM>, light is carried predominantly in the top waveguide <NUM> (although a small fraction of the optical mode may still be carried in the bottom waveguide <NUM>). In the active layer <NUM> of the top waveguide, the light can be, e.g., amplified or absorbed. In a second waveguide transition at the end of the overlap region, where the top waveguide <NUM> tapers down, light is coupled back into the bottom waveguide <NUM>. As can be seen in <FIG>, at the start of the overlap region between the two waveguides <NUM>, <NUM>, the top waveguide <NUM> is only slightly wider than the bottom waveguide <NUM>. In the center region <NUM>, the top waveguide <NUM> may be significantly wider, as shown in <FIG>. Apart from the location of the tapers <NUM>, <NUM> in the top waveguide <NUM>, the photonic structure <NUM> may be similar, e.g., in dimensions and materials, to the photonic structure <NUM> of <FIG>.

Note that, in <FIG>, the waveguide tapers <NUM>, <NUM> are shown with non-linear taper profiles; that is, the width of the top waveguide <NUM> varies non-linearly with position in the longitudinal direction along the waveguide. By contrast, <FIG> shows, for illustration purposes only, linear waveguide tapers <NUM>, <NUM> in the bottom waveguide <NUM>. In accordance with various embodiments, waveguide transitions are designed to have non-linear tapers, regardless of the waveguide (i.e., top or bottom waveguide) that includes the taper.

While <FIG> depict photonic structures with tapered waveguide transitions on both ends, as may be used, e.g., to couple light into and out of a heterogeneously implemented optical modulator (e.g., an electro-absorption modulator) or amplifier, the embodiments contemplated herein also encompass heterogeneous photonic structures that include only a single waveguide transition, e.g., to couple light at the input or output of a photonic circuit from or to a photonic device such as a laser or photodetector. Also, to the extent a photonic structure includes two waveguide transitions, they need not necessarily be symmetric, or even both be tapered. Further, although the use of waveguide transitions has been described in the context of heterogeneous integration of different materials, the principles for designing and making tapered waveguide transitions also apply to transitions between two waveguides of the same material, e.g., two silicon waveguides in adjacent waveguide layers of a multi-layer photonic circuit.

Moreover, while <FIG> illustrate waveguide tapers in either the top or the bottom waveguide, waveguide transitions may also, in accordance with other embodiments, include tapers in both the top waveguide and the bottom waveguide, e.g., arranged in an overlapping fashion such that one of the tapers increases in width as the other one decreases in width. In the following, it will be explained how the taper profile can be optimized for the structure of the waveguide transition to achieve good coupling between the waveguides and minimize scattering losses. While this description assumes only one of the waveguides to be tapered, those of ordinary skill in the art will know how to adapt the design methods to waveguide transitions with two overlapping tapers.

A waveguide transition usually serves to couple light from the fundamental optical mode of one waveguide to the fundamental optical mode of the other waveguide. In the transition region, a fundamental hybrid mode, or "supermode," across both waveguides emerges. However, the fundamental hybrid mode can excite undesired higher-order hybrid modes as a result of spatial overlap between the modes. This coupling of light into the undesired higher-order hybrid modes amounts to scattering losses along the waveguide transition. The losses can be predicted by computing the overlap integral between the fundamental and higher-order hybrid modes, in this context called the "scattering rate" S: <MAT> where E<NUM> is the fundamental hybrid mode, Ei is the i-th higher-order mode, and Δneff is the effective index difference of the combined waveguide structure between the fundamental and i-th higher-order mode. The calculation can, in principle, iterate over multiple higher-order modes of increasing order (i = <NUM>, <NUM>,. ), and the contributions of all of those higher-order modes can be summed over to determine the total scattering rate. In practice, however, it is often sufficient to compute losses only for the first-order mode (i = <NUM>), or the first few higher-order modes, as the overlap between the fundamental mode and the higher-order modes diminishes quickly, and the effective index difference increases, towards increasing order i, such that loss contributions beyond that of the first or first few higher orders become negligible.

The waveguide modes can be computed from the cross-sectional waveguide structure, e.g., using a numerical waveguide mode solver. Mode solvers are well-known in the art and provided as part of various commercially available software packages, including, e.g., MATLAB® from MathWorks, or the DEVICE Multiphysics Simulation Suite from Ansys-Lumerical. In a tapered waveguide transition, the cross-sectional structure at each point along the length of the waveguide can be characterized by the waveguide width at that point, in conjunction with other dimensions as well as material properties that are constant along the waveguide.

<FIG> is an example graph <NUM> illustrating the width-dependent scattering rate of a waveguide transition for nominal design parameters and multiple process corners in accordance with one embodiment. In this example, the waveguide transition is between a tapered silicon rib waveguide and a III-V waveguide. The silicon waveguide width measured in micrometers is shown along the abscissa (or x-axis), and the scattering rate is provided in arbitrary units along the ordinate (or y-axis). Curve <NUM> is the scattering rate computed for the nominal design parameters. Curves <NUM> and <NUM> illustrate the scattering rate for process corners corresponding to an increase or decrease, respectively, of the layer height of the silicon slab underneath the rib (e.g., slab <NUM> in <FIG>); as can be seen, a thinner slab causes a significant increase in the scattering rate. Curves <NUM>, <NUM> show the scattering rate for process corners associated with an increase or decrease, respectively, of the gap between the silicon rib waveguide and the III-V waveguide, that is, the thickness of any bonding layer and/or insulating layer underneath the III-V waveguide; a decrease in the gap likewise increases the scattering rate. As shown in curves <NUM>, <NUM>, which illustrate the scattering rate for process corners associated with an increase or decrease, respectively, in the height of the silicon waveguide rib, this design parameter shifts the curve slightly, but affects the magnitude of the scattering rate to a lesser extent. Curves <NUM>, <NUM>, corresponding to the scattering rate for process corners associated with an increase or decrease, respectively, of the width of the III-V waveguide, show a substantial increase of the scattering rate with increased width. In general, design parameters that may affect the scattering rate at a waveguide transition include, for example and without limitation, the waveguide widths of the bottom and/or top waveguide, the etch depth of a bottom and/or top rib waveguide, the thickness of the bottom and/or top waveguide, the refractive index of the top and/or bottom waveguide, the distance between the bottom and/or top waveguide (e.g., as is driven by the insulated-layer thickness), and the lateral misalignment between the bottom and top waveguides.

The scattering loss incurred along a waveguide taper for a given width increment dw is proportional to the width gradient <MAT> along the length z of the waveguide as well as the width-dependent scattering rate S(w). For a given total change in width Δw and a given taper length L, the lowest possible scattering losses can be achieved by choosing a gradient as a function of width that is inversely proportional to the scattering rate: <MAT> (or, equivalently, <MAT>). With this taper profile, the total change in width and the taper length are related according to: <MAT> As illustrated in <FIG>, however, the scattering rate S(w), although determinable for a given waveguide transition design, varies significantly with changes in the design parameters. According to the claimed invention, these variations are taken into account when computing the waveguide taper profile.

<FIG> is a graph <NUM> illustrating an envelope <NUM> of the width-dependent scattering rate of a waveguide transition for nominal design parameters and multiple process corners, providing an upper bound on the scattering rate of the waveguide transition, in accordance with one embodiment. Similarly to <FIG>, graph <NUM> illustrates the width-dependent scattering rate S(w) associated with a waveguide transition between a tapered silicon rib waveguide and a III-V waveguide for multiple process cases, including for a set of nominal parameter values (curve <NUM>) as well as a set of parameter values associated with various process corners. The process corners correspond to lower and upper bounds on the gap between the two waveguides (curves <NUM>, <NUM>), the index of refraction of the III-V waveguide (curves <NUM>, <NUM>), the height of the rib waveguide (curves <NUM>, <NUM>), and the height of the silicon slab (curves <NUM>, <NUM>). The envelope <NUM>, as the term is used herein (not in the strict geometric sense of "envelope," although similar in nature), is a curve that provides an upper bound to all process cases collectively by determining, at each waveguide width, the maximum scattering rate across all process corners and linearly interpolating between local maxima across waveguide width. As such, the envelope captures the worst-case scattering scenario across the range of all fabrication variations within acceptable margins. According to the claimed invention, the taper profile is computed based on the envelope <NUM> of the scattering rates, rather than based on the scattering rate for nominal design parameter values (or any other particular set of values).

Note that, in the depicted case, only one design parameter at a time is varied. To strictly account for all fabrication variations, computations of the scattering rate for cases where two or more design parameters vary simultaneously from the nominal values may also be included. Such cases will, however, be rarely encountered in practice, and accounting for them explicitly is, thus, usually unnecessary. Instead, by taking a linear-interpolation envelope, the design will effectively also be tolerant to simultaneous medium variations in multiple parameters. The adequacy of the envelope can be tested, e.g., with Monte-Carlo simulations for a set of design parameter variations chosen from known statistics of the design parameter variations in fabrication, which could provide assurance that a satisfactory number of scattering rates fall within the envelope. Alternatively, the adequacy of the envelope can be implicitly validated by simulations performed on the final taper design, as explained below with reference to <FIG>.

<FIG> is a graph <NUM> showing a non-linear waveguide taper profile <NUM> determined based on the envelope <NUM> shown in <FIG>, in accordance with one embodiment. For comparison, a linear taper profile <NUM> is also shown. The taper width in micrometers, plotted as a function position z along the longitudinal axis of the taper (in arbitrary units), increases from about <NUM> to about <NUM>; <FIG> indicates this width range with the dashed line <NUM>. The non-linear profile exhibits steep gradients, corresponding to a sharp increase in width, at the beginning and end of the taper, where the scattering rate is low, while the width varies slowly in the middle of the taper, where the scattering rate is high. The very gradual change in width over most of the length of the taper balances the high scattering rate at medium taper widths, which can improve overall performance.

While the foregoing description refers to waveguide transitions including a taper in either the bottom or the top waveguide, the taper design method can be straightforwardly extended to transitions between two tapered waveguides. To do so, the scattering rate may be computed as a function of the widths of both waveguides (e.g., silicon width and III-V width), resulting, for each set of design parameters, in a contour map or other three-dimensional representation (with scattering rate along the z-axis vs. waveguide widths along the x- and y-axes). Multiple such contour plots for multiple respective sets of design parameters (e.g., for the nominal design and multiple process corners) will take the place of the two-dimensional curves of <FIG>. An envelope Z(x, y) can be defined over the contour plots. A single line y = f(x) in the x-y plane spanned by the two waveguide widths, representing a particular combined taper design for the top and bottom waveguides, may then be determined so as to minimize the envelope area under Z(x, f(x)).

<FIG> is a graph <NUM> illustrating the simulated transmission of a tapered waveguide transition as a function of taper length for multiple process corners, in accordance with one embodiment. The taper length is indicated along the abscissa in micrometers. Along the ordinate, the transmission of the waveguide transition, which measures the fraction of optical power that is coupled from the fundamental mode of one waveguide into the fundamental mode of the other, is provided. The different curves correspond to different process cases that reflect a range of values of the design parameters, but are all computed for the same non-linear taper profile (such as the profile <NUM> shown in <FIG>), scaled to the respective total taper length for each point along each curve. The simulations can be performed, e.g., with the beam propagation method (BPM), eigen-mode expansion (EME), or finite-element time domain (FDTD) method, which are techniques, well-known to those of ordinary skill in the art, that simulate the propagation of light in slowly varying optical waveguides. The family of curves shown in graph <NUM> may be used to determine, for a specified length of the taper, the minimum of the transmission across the range of simulated cases, which provides a lower bound below which transmission is, in practice, unlikely to fall. In other words, the simulations allow specifying a virtually guaranteed transmission performance for a waveguide transition having the computed taper profile and specified length. Conversely, it is possible to specify a threshold transmission value, and read off the length that the taper should have to ensure that the transmission exceeds the threshold for all expected process variations. For example, with reference to <FIG>, to achieve a transmission of about <NUM>% or higher, the waveguide should have a length of about <NUM> or more.

<FIG> is a flow chart of a method <NUM> for designing a heterogeneous waveguide transition with a fabrication-tolerant non-linear waveguide taper, in accordance with various embodiments. The method <NUM> begins, in act <NUM>, with the specification of multiple sets of parameter values for parameters characterizing the waveguide transition, such as layer thicknesses, waveguide dimensions, and waveguide materials and/or material properties (e.g., the refractive index). One set of parameter values corresponds to the nominal waveguide transition design. The other sets of parameter values capture expected fabrication variations from the nominal values, i.e., the process corners (corresponding to the extremes of the variations at the outer limits of the tolerance margins). In act <NUM>, the scattering rate as a function of waveguide width is computed for each of the multiple sets of parameter values. This computation may be performed, e.g., by a computer using software such as, or including, a mode solver, based on the parameter values received as input in act <NUM>. The parameter values may, e.g., be provided to the computer by a human operator via a user interface, or read in from a design file stored in memory. Once the waveguide-width-dependent scattering rate has been computed for all sets of parameter values, their envelope (e.g., as shown in <FIG>) is determined in act <NUM>. This step will generally be performed automatically based on suitable program instructions (although it could, in principle, also be done manually by the user). From the envelope, a taper profile (arbitrarily scaled) is then computed in act <NUM>. Optionally, a threshold transmission value may be specified in act <NUM>, e.g., by the user, and the minimum taper length meeting the condition that the transmission exceeds the threshold value may be determined in act <NUM> by simulating the taper based on the computed taper profile for various lengths (e.g., as shown in <FIG>) with suitable simulation software, and identifying the lower taper-length cut-off associated with the desired transmission. The taper profile can then be scaled to the determined taper length (act <NUM>), which completes the taper design process.

<FIG> is a flow chart of a method <NUM> of making a heterogeneous waveguide transition with a fabrication-tolerant non-linear waveguide taper, in accordance with various embodiments. The method <NUM> begins by specifying the general design of the waveguide transition in act <NUM> (corresponding to the nominal parameter values provided in act <NUM> of method <NUM>), and determining the taper profile and length, in act <NUM>, in accordance with acts <NUM>-<NUM> of method <NUM>. To make the waveguide transition, a semiconductor device layer, such as the silicon device layer of an SOI substrate, is first patterned to form the first waveguide of the transition in act <NUM>. Next, a second semiconductor layer, e.g., of III-V material or another compound semiconductor, is deposited above the patterned first layer in act <NUM>. For example, a III-V die may be bonded to the silicon or other semiconductor device layer in the region above the first waveguide. In act <NUM>, the second semiconductor layer is patterned to form the second waveguide. The patterning of the first and second layers is done in accordance with relevant parameters of the design specified in act <NUM> (e.g., waveguide widths), and either the first or the second semiconductor layer is patterned based on the computed taper profile, depending on which of the two waveguides is to be tapered. In some embodiments, overlapping tapers are created based on computed taper profiles for both waveguides. The patterning in acts <NUM>, <NUM> may be performed using conventional lithographic patterning, followed by etching and related processing steps (such as applying an oxide fill to the patterned device layer prior to bonding the die).

<FIG> is a block diagram of a computer system <NUM> for performing operations implementing the method of <FIG>, which is helpful to understand the invention as it provides a context in which the invention can operate. The machine may operate as a single, standalone device, or may be connected (e.g., networked) to other machines. In a networked deployment, the machine may operate in the capacity of a server or a client machine in server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. While only a single machine is illustrated, the term "machine" shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the computational operations discussed herein. The example computer system <NUM> includes one or more processors <NUM> (e.g., a central processing unit (CPU), a graphics processing unit (GPU) or both), a main memory <NUM> and a static memory <NUM>, which communicate with each other via a bus <NUM>. The computer system <NUM> may further include a video display unit <NUM> (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)). The computer system <NUM> may also include an alphanumeric input device <NUM> (e.g., a keyboard), a cursor control device <NUM> (e.g., a mouse), a disk drive unit <NUM>, a signal generation device <NUM> (e.g., a speaker), and a network interface device <NUM> to communicate via a network <NUM>.

The disk drive unit <NUM> includes a machine-readable medium <NUM> storing one or more sets of instructions and data structures (e.g., software) <NUM> embodying or utilized by any one or more of the methodologies or functions described herein. The instructions <NUM> may also reside, completely or at least partially, within the main memory <NUM> and/or within the processor <NUM> during execution of the instructions <NUM> by the computer system <NUM>, the main memory <NUM> and the processor <NUM> thereby also constituting machine-readable media. The sets of instructions may include, for example, a mode solver, a simulation program to simulate light propagation along and coupling between the waveguides of the waveguide transition, and/or a main program configured to receive the parameters characterizing the waveguide transition design and process corners, and determine the taper profile and length, using the mode solver and simulation program.

While the machine-readable medium <NUM> is shown in an example embodiment to be a single medium, the term "machine-readable medium" may include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more instructions or data structures. The term "machine-readable medium" shall also be taken to include any tangible medium that is capable of storing, encoding, or carrying (which may be collectively termed conveying) instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present teachings, or that is capable of storing, encoding or carrying (which may be collectively termed conveying) data structures utilized by or associated with such instructions. The term "machine-readable medium" shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media. Specific examples of machine-readable media include non-volatile memory, including by way of example semiconductor memory devices, e.g., Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; CD-ROM and DVD-ROM disks, or other data-storage devices. The term "machine-readable medium" shall accordingly be taken to include, but not be limited to, transmission media such as carrier waves and transmission signals which can convey instructions between computer systems or between components of a single computer system. In addition the terms "machine readable medium" can be used interchangeably with "computer-readable medium".

Therefore, from one perspective, there has been explained that a fabrication-tolerant non-linear waveguide taper for a waveguide transition can be designed by computing the scattering rate associated with the waveguide transition as a function of waveguide width of the waveguide taper for each of multiple sets of parameter values characterizing the waveguide transition ( a set of nominal parameter values and sets of parameter values associated with process corners representing process variations from the nominal parameter values), determining an envelope of the computed width-dependent scattering rates, and computing a non-linear taper profile of the waveguide taper based on the envelope. Light propagation and coupling along the waveguide transition may further be computationally simulated for the multiple sets of parameter values to determine a minimum transmission value associated with the waveguide transition for a specified taper length, and/or to determine a minimum taper length at which the transmission values associated with the waveguide transition exceed a specified threshold transmission value.

Claim 1:
A method of making a waveguide transition between two waveguides, the waveguide transition comprising a waveguide taper, the method comprising:
specifying multiple sets of parameter values for parameters characterizing the waveguide transition, wherein the multiple sets of parameter values comprise a set of nominal parameter values and a set of parameter values associated with process corners representing process variations from the nominal parameter values;
computing a scattering rate as a function of waveguide width of the waveguide taper for each of the multiple sets of parameter values;
determining an envelope of the scattering rates for the multiple sets of parameter values, wherein the envelope is a curve that provides an upper bound to all process cases collectively by determining, at each waveguide width, the maximum scattering rate across all process corners and linearly interpolating between local maxima across waveguide width;
computing a non-linear taper profile of the waveguide taper based on the envelope; and
fabricating the waveguide transition based on the computed non-linear taper profile.