[ 0014 ] fig1 illustrates a partial cross - section of a semiconductor workpiece ( not to scale ) during an early stage in fabricating a vertical taper , according to one embodiment of the present invention . the workpiece includes a semiconductor substrate 10 , a cladding layer 12 , a core layer 14 , and a protective layer 16 . in some embodiments , core layer 14 is formed from a semiconductor material while cladding layer 12 is formed from an insulating material ( e . g ., oxide ) in which the refractive index n 1 of core layer 14 is greater than the refractive index n 2 of cladding layer 12 . in this embodiment , core layer 14 is formed from silicon and cladding layer 12 is formed from silica ( sio 2 ). protective layer 16 , in some embodiments , is formed from oxide . in other embodiments in which core layer 14 is formed from silica , protective layer 16 can be formed from a silicon nitride ( e . g ., si 3 n 4 ). in addition , cladding layer 14 could also be formed from nitride . more particularly , cladding layer 12 is formed between semiconductor substrate 10 and core layer 14 . in this embodiment , semiconductor substrate 10 is formed from silicon ; however , semiconductor substrate 10 can be formed from different semiconductor materials in other embodiments ( e . g ., gallium arsenide ). further , in this embodiment , cladding layer 12 is formed from a silicon oxide ( e . g ., silica ), although in other embodiments cladding layer 12 can be formed from other non - conductive materials . in one embodiment , semiconductor substrate 10 , cladding layer 12 and core layer 14 are formed using known silicon on insulator ( soi ) wafer fabrication processes . for example , a buried oxide layer can be formed using known oxygen implantation processes to serve as cladding layer 12 . cladding layer 12 , in this embodiment , has a thickness of about 1 μm , but can range from about 0 . 35 μm to 2 μm in other embodiments . further , in this embodiment , core layer 14 is a silicon layer with a thickness of about 2 . 5 μm , but can have a thickness ranging from about 1 μm to 10 μm in other embodiments . protective layer 16 , in one embodiment , is an oxide layer with a thickness of about 2 μm , but can range from about 0 . 5 μm to about 5 μm in other embodiments . the oxide of this embodiment of protective layer 16 can be formed using any suitable known process such as , for example , a low temperature oxide ( lto ) process . although an oxide protective layer is described , other materials can be used in other embodiments . for example , materials having a lower chemical mechanical polishing ( cmp ) removal rate for a selected cmp process ( e . g ., polishing pad and slurry ) that the material of core layer 14 may be suitable for protective layer 16 . fig1 a illustrates a top view of the resulting structure ( not to scale ), with protective layer 16 being the only layer that is visible . [ 0019 ] fig2 illustrates a partial cross - section of the semiconductor workpiece ( not to scale ) during another stage , according to one embodiment of the present invention . in this stage , protective layer 16 ( fig1 ) is patterned to have an opening 21 , shown as patterned protective layer 16 a in fig2 . in some embodiments , known photolithography techniques are used to form patterned protective layer 16 a . opening 21 defines a region in which the vertical taper will be formed . in this embodiment , opening 21 is rectangular in shape , although other shapes may be used in other embodiments . fig2 a illustrates a top view of the resulting structure ( not to scale ), with patterned protective layer 16 a being visible . in addition , a portion of core layer 14 is exposed via opening 21 in patterned protective layer 16 a . [ 0020 ] fig3 illustrates a partial cross - section of the semiconductor workpiece ( not to scale ) during another stage , according to one embodiment of the present invention . in this stage , a chemical mechanical polishing ( cmp ) process is performed on the structure of fig2 . further , in this embodiment , the cmp process is performed so that “ dishing ” occurs , as described below . as is well known in the art of cmp , “ dishing ” can occur when the surface being polished includes a trench or via filled with a material that is different from the material surrounding the trench or via . dishing typically occurs during a cmp operation when the material within the trench or via can be removed at a faster rate than the material surrounding the trench or via . this may occur when the surface is “ over polished ”. dishing causes the material in the trench or via to have a concave surface topology . in the context of this embodiment , a cmp operation is performed on the structure of fig2 using a recipe that causes dishing . as a result , the cmp operation forms a depression 31 in the portion of the core layer that is exposed by opening 21 ( fig2 ). the core layer with depression 31 is indicated in fig3 as polished core layer 14 a . in one embodiment , the cmp “ recipe ” is designed to increase the normally undesirable “ dishing ” of the exposed portion of core layer 14 . for example , in an embodiment in which the core layer is formed from silicon , a silicon - selective slurry can be used ( i . e ., a slurry that achieves a higher removal rate for silicon relative to its removal rate for the material of patterned protective layer 16 a ). the hardness of the polishing pad , polishing pressure , rotation rate , polishing time and / or other cmp parameters can be optimized to achieve the desired concave shape for depression 31 . for example , in one embodiment the cmp recipe is designed so that the dishing causes an upper portion of the sidewall of depression 31 to have a sloped topography that is desired for the vertical taper . in some embodiments , some material is removed during the cmp operation from the upper portion of patterned protective layer 16 a ( fig2 ) and from the sidewalls of opening 21 ( fig2 ). the resulting structure of the protective layer is indicated as polished protective layer 16 b in fig3 . in other embodiments , the amount of material removed from the protective layer during cmp is not significant when compared to the material removed from core layer 14 . [ 0024 ] fig3 a illustrates a top view of the resulting structure ( not to scale ) showing polished protective layer 16 b . in addition , depression 31 of patterned core layer 14 a is visible through opening 21 ( which in this embodiment is widened or eroded by the cmp operation ). [ 0025 ] fig4 illustrates a partial cross - section of the semiconductor workpiece ( not to scale ) during another stage , according to one embodiment of the present invention . in this stage , polished protective layer 16 b ( fig3 ) is removed . in one embodiment , a selective etching process is used to remove polished protective layer 16 b while leaving polished core layer 14 a essentially the same as it was before the etching process was performed . in an alternative embodiment , patterned protective layer 16 a ( fig2 ) is removed during the cmp operation . for example , the protective layer can be relatively thin . in addition , the cmp recipe can be designed to remove the protective layer at a rate that results in the protective layer being cleared when depression 31 in the core layer has reached the desired shape . an etching mask 41 is then formed on polished core layer 14 a as shown in fig4 . for example , etching mask 41 may be formed from si 3 n 4 and then patterned using known photolithography techniques to mask a portion of polished core layer 14 a ( including a portion of depression 31 ). etching mask 41 defines a taper to be formed at an end of a waveguide . more specifically , etching mask 41 covers the portion of depression 31 that has the sloped topography that is desired for the vertical taper . [ 0028 ] fig4 a illustrates a top view of the resulting structure ( not to scale ). as shown , etching mask 41 is visible , along with a portion of polished core layer 14 a of core layer 14 . a portion of depression 31 is indicated in dashed lines in fig4 a . [ 0029 ] fig5 illustrates a partial cross - section of the semiconductor workpiece ( not to scale ) during still another stage , according to one embodiment of the present invention . in this stage , polished core layer 14 a ( fig4 ) is etched and etching mask 41 ( fig4 ) is removed . in one embodiment , an etchback process is used to etch the portion of polished core layer 14 a ( fig4 ) left uncovered by etching mask 41 ( fig4 ). for example , in one embodiment , a photoresist is spun onto the structure of fig4 . an etching process is then performed that etches the material of the photoresist and core layer at substantially the same rate , while being nonselective for the material of etching mask 41 . the etching process is performed to remove an “ excess ” portion polished core layer 14 a ( fig4 ) to form a waveguide with a vertical taper at an end of the waveguide . in this embodiment , the portion of polished core layer 14 a ( fig4 ) left uncovered by etching mask 41 ( fig4 ) is etched until it is planarized , which is indicated in fig5 as portion 51 of etched core layer 14 b . further , in this embodiment the upper surface of portion 51 of etched core layer 14 b is level with the portion of the surface of depression 31 ( fig4 ) that is aligned with the sidewall of etching mask layer 41 ( fig4 ). consequently , this etching process changes depression 31 ( fig4 ) into a sloped region 31 a as indicated in fig5 . the resulting thickness of the planarized portion of etched core layer 14 b is the desired thickness of the waveguide being formed . etching mask 41 is then removed . the resulting structure is shown in fig5 and 5a . this stage of the vertical taper fabrication process represents a significant improvement over conventional processes that etch silicon to form the vertical taper . for example , as previously described , etching the core layer to form the sloped surface can undesirably roughen the sloped surface , increasing loss . in contrast , in accordance with embodiments of the present invention , the sloped surface of the vertical taper is not etched . rather , the sloped surface is polished using a cmp process , which can result in a smoother sloped surface . consequently , the vertical taper formed by cmp of the core layer could generally have less loss than one that is formed by etching . in subsequent processing steps , etched core layer 14 b ( including sloped region 31 a ) can be patterned and etched to form a waveguide . in addition , this patterning and etching process can form a lateral taper ( not shown ) in the core layer 14 . a lateral taper can make coupling the waveguide to another waveguide or optical fiber that has a larger cross sectional area than the waveguide formed in core layer 14 . although not shown , another cladding layer ( e . g . oxide , nitride , etc .) can be formed over the structure shown in fig5 and 5a in subsequent processing steps . [ 0033 ] fig6 illustrates a perspective view of a section shown in fig5 after etched core layer 14 b ( fig5 ) has been patterned and etched to form part of a waveguide of a plc . the core layer is shown as patterned core layer 14 c in fig5 . in this embodiment , the waveguide is a rib waveguide . in operation , for example , an optical fiber can be coupled to the wide end 61 of the taper structure so that an optical signal can propagate from the optical fiber into portion 51 of patterned core layer 14 c of the waveguide . sloped region 31 a causes the optical signal to propagate downwards as the optical signal propagates toward portion 51 of patterned core layer 14 c . further , although embodiments for vertical taper applications are described above , other embodiments may be used in other mode converter applications as well . [ 0036 ] fig7 illustrates a system 70 in which a waveguide taper according to embodiments of the present invention can be used . system 70 includes an optical signal source 71 connected to one end of an optical fiber 72 . the other end of optical fiber 72 is connected to a plc 73 that includes a taper 74 . taper 74 is fabricated according to one of the embodiments described above . for example , when the taper is implemented as shown in the embodiment of fig6 wide end 61 would be used to connect plc 73 to the end of optical fiber 72 . in one embodiment , plc 73 is implemented in an integrated circuit . other embodiments may have one or more other tapers ( not shown ) that are essentially identical in structure to taper 74 . reference throughout this specification to “ one embodiment ” or “ an embodiment ” means that a particular feature , structure , or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention . thus , the appearances of the phrases “ in one embodiment ” or “ in an embodiment ” in various places throughout this specification are not necessarily all referring to the same embodiment . furthermore , the particular features , structures , or characteristics may be combined in any suitable optical manner in one or more embodiments . in addition , embodiments of the present description may be implemented not only within a semiconductor chip but also within machine - readable media . for example , the designs described above may be stored upon and / or embedded within machine readable media associated with a design tool used for designing semiconductor devices . examples include a netlist formatted in the vhsic hardware description language ( vhdl ) language , verilog language or spice language . some netlist examples include : a behavioral level netlist , a register transfer level ( rtl ) netlist , a gate level netlist and a transistor level netlist . machine - readable media also include media having layout information such as a gds - ii file . furthermore , netlist files or other machine - readable media for semiconductor chip design may be used in a simulation environment to perform the methods of the teachings described above . thus , embodiments of this invention may be used as or to support a software program executed upon some form of processing core ( such as the cpu of a computer ) or otherwise implemented or realized upon or within a machine - readable medium . a machine - readable medium includes any mechanism for storing or transmitting information in a form readable by a machine ( e . g ., a computer ). for example , a machine - readable medium can include such as a read only memory ( rom ); a random access memory ( ram ); a magnetic disk storage media ; an optical storage media ; and a flash memory device , etc . in addition , a machine - readable medium can include propagated signals such as electrical , optical , acoustical or other form of propagated signals ( e . g ., carrier waves , infrared signals , digital signals , etc .). in the foregoing specification , the invention has been described with reference to specific exemplary embodiments thereof . it will , however , be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention as set forth in the appended claims . the specification and drawings are , accordingly , to be regarded in an illustrative rather than a restrictive sense .