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UNIGIT RIGOROUS GRATING SOLVER VERSION 2.01.04 USER

1. ANA NANAN A orous grating solver ARARNAR E UNIGIT Layer Editor Name Layer Layer Type Maia a IU Thickness 10 2 um Refractive Index Medium 1 Direct Input Real Part 1 500 Imaginary Part 0 000 Edit Refractive Index Medium 2 Direct Input Real Part 1 000 Imaginary Part 0 000 E dit Polygon Points relative Layer iz uen x 0 300 L 025 r 4 i i 0200 4 t 4 4 L 0 150 2 J L 4 4 I L LU 0 100 2 J L 4 L DN gt gt gt A S x z i U lo lo ow J AA 0 000 0250 0 300 0150 1000 Insert ieplace Delete AD D jm Cancel Fig 22 Layer editor for 1D RF Polygon layers A polygonal RF layer is characterized by two materials that are separated by a polygonal interface The specification of this layer type 1s as follows First one has to specify the refraction indices of the materials above medium 1 and below medium 2 the interface by means of the respective refraction index editor Second the thickness of the layer has to be fixed In the context of a RF layer the thickness corresponds to the absolute peak to valley value of the profile Actually the entered profile is renormalized with this value Next this interface profile has to be defined T
2. o Single Files means that each diffraction order is saved in a separate file The file location is specified as before however the name is used as a template and completed by different attachments depending on the order whether it 1s reflection or transmission the polarisation and the type of output information It also depends on which solver was specified 1D or 2D Basically the following coding is used Assume the basic name as specified in the text box is test Then the file name is testOXO Y MPP where OX is the diffraction order in x direction Copyright by Optimod 56 64 November 7 2014 sip nnd LI O Emu X HRR mo versatile rigorous grating solver OY is the diffraction order in y direction is obsolete for 1D case and is skipped there Mis the mode 1 e R for reflection or T for transmission PP is the polarisation first P for input and second P for output P can either be E for TE or M for TM polarisation To give an example cross polarisation from TE to TM is characterized by PP 2 EM whereas TE polarisation is assigned by PP EE The second P is obsolete for 1D classic case there is no cross polarisation and 1s thus skipped As an example test 0ml tmm means transmission of TM in 0 1 order x y e Selection of the Mode checkbox transmission reflexion e Selection whether depend the results to existing file s or create new one s e Specification of the output format o Se
3. eo UNIGIT RIGOROUS GRATING SOLVER VERSION 2 01 04 Installation for Version 2 01 04 Copyright by OP TMOG Jena Germany Developed by Optimod Ricarda Huch Weg 12 D 07745 JENA GERMANY phone 49 03641 825944 cell phone 49 162 9067015 email support unigit com Copyright by Optimod 1 64 November 7 2014 HERE C ONE rrrrrrrrr AN ANANACA NANANES a Nancanananar gorous i r L gt PE EL AXES HE and d in LLL anta nda Change Record changes versus version 2 01 03 Section s Page s Parallel Editor expanded into General Settings profiles 5 1 5 e 1 implemented Color assignment for materials included via color table 3 2 and 6 19 and 51 Layer Editor for C method sinusoidal layer changed C method stack editor changed 42 o Figure with definition of angles added 4 5 Python link implemented 2 9 and 3 5 17 and 20 Layer Editor for C method polygon layer changed 4 2 Copyright by Optimod 2 64 November 7 2014 II bui gt pan ELE B AS a at ud d E i LDIDIIITIIIIIUCETY EPPP apapa hil eerie EN ALEA A A LII E ru E s E met rai T VH TERREA versatile rigorous grating solver tp iv l EEEH EH Table of Content AA MER tise 2 changes yersus verion OU T 2 je 3 e DOC COs up see anni eens EUMDE
4. If it is not needed anymore it should be deleted again The coefficient information 1s stored in one file per dispersion formula with the related file name These files are also located in the folder Unigit NKData and can be identified by the file extension nkk A list of the available dispersion formulas 1s shown below Copyright by Optimod 53 64 November 7 2014 EREGRE RE HAN E r E E r CUPE BEANE CT i mmm E i IZ HARAN a ELIT CrN i i st mos y TT i ww gi L4 ANANANA GA i as o Bi L LIN o m L anni nar E E RANANAF nma nat LE Li a Anu D SAGAS 4 MJ I a M En o y y B E A SEAR Nn Tw we bulis x a nuar I v LLI Stenentacus a n Lis A i t t LEE LI LI C Ti Wem tae 4 LE 4 T P r ra 24 L 2 a ss ras LI AI P Buchdahl 4 coefficients required n1 nd fn bin bd any o With A R A 0 001 A 24 ano 1 2 54 Cauchy 3 coefficients required n1 n3 11 11 de E P ang k7O p t t Drude 3 coefficients required n1 n3 n 405 A B ong k 405 A B with 2 n3 _ a2 pe Ban A JB snd l D ui EFD gan Dono Lorentz 4 coefficients required n1 nad 3 n n tk nA L UE fs fly E and with A A4 ni and B A nj Quad 5 coefficients required n1 n6 nanta Ara anc k n ta Ata A Y Copyright by Optimod 54 64 November 7 2014 S
5. LLILIDELDLLL Fig 18 Cross section of a RCW A grating Example 1 shown in Fig 18 visualizes the stack as given in the stack editor in Fig 17 Obviously it is an RCWA example As can be realized from the sinusoidal layer on top red the slicing is fully included In contrast a C method example is given below Fig 19 shows the cross section of the stack in Fig 15 Copyright by Optimod 26 64 November 7 2014 0 250 Cancel Fig 19 Cross section of the stack as listed in fig 15 Copyright by Optimod 27 64 November 7 2014 i HI RRRRRERRRREM Errr 5 Layer Editor 5 1 Layer Editor 1D RCWA amp Rayleigh Fourier The layer editor can be activated from within the stack editor Its appearance and functionality depends on whether the 1D classical or conical or 2D option is selected If activated by the INSERT button within the stack editor the layer editor will appear as shown in the screen shot of Fig 20 UNIGIT Layer Editor xi Name no name Layer Type IMA v Thickness 1 um Refractive Index Medium 1 Direct Input Real Part 1 000 Imaginary Part 0 000 Ts Cancel Fig 20 Layer editor for 1D layers general First select the layer type from the drop down box as shown below JUNIGIT Layer Editor Name no name Layer Type Thin Film RF Polygon Layer Direct Input RF Sinus Layer RCWA Slice Hard Transition RCWA Slice Soft
6. 1 6 Composite Polygon Layer slicing In order to alleviate the assembling of complicated interfaces the composite or slicing layers were implemented Basically there are two types available that differ by the interface description The polygon slicing layer is characterized by the specification of the interface by means of a set of points that are connected by straight lines Thus the input scheme is widely similar to those of the RF polygon layer After selecting this layer type the layer editor shows up as depicted in Fig 28 UNIGIT Layer Editor E X Mame Polygon Layer Type Slicing Polygon Thickness 0 22 pum Refractive Index Medium 1 Direct Input Real Part 1 000 Imaginary Part 0 000 Edit Hefractian Index Medium z l l Calculate Slicing Direct Input Real Part 2 000 Imaginary Part 0 000 7 Show Sliced Profile Polygon Paints relative Layer z Ue TENE X Ai 0 0000 0 0000 0 2500 0 3000 0 7500 0 3000 1 0000 0 0000 M z o i 0250 0 500 0750 1 000 Insert Replace Remove 0 o Deltas 0 02 Delta 10 02 Slicing File A Ee E Cancel Fig 28 Layer editor for 1D composite polygon layer a k a slicing polygon First the same specifications like for the RF polygon layer step 1 thru 3 have to be done The big difference in comparison to RF layers however consists in the further processing of the layer 1 e the solution of the diffraction problem While for th
7. November 7 2014 rt H ia 8 UNIGIT Projects 8 1 General Remarks Unigit project files have been introduced to facilitate the organization of complex modeling projects as well as to give some support in retrieving and reconstructing simulations dated back some time Concurrently it provides an appropriate mean to avoid time consuming reruns of the UNIGIT solver in order to obtain a different output format for the same application example Suppose for instance you have calculated the diffraction efficiencies for a complex 2D example that took several hours Later 1t turns out that you also need the phase information Then it would have been a good idea to activate the project file generation in the first run see section 7 2 Unigit project files can load instead of stack files see Fig 50 It possesses the extension Mame nderungs Typ Gr e 2 dielgrat 1d upr Fig 50 Selection of an Em project file After selecting an UPR file UNIGIT switches from its regular mode into the project retrieval mode This becomes obvious by two features Copyright by Optimod 60 64 November 7 2014 First the group in upper right corner changes its 3 name from Stack to Project and secondly the START button changes its name into Extract Results In addition the buttons in the project control group middle right are enabled see Fig 51 uan UNIGIT Central Control Board um Loue EE Wavelength in
8. Result in C Programme O ptimod Unigit Fesults Achim test Delete File Notepad Copyright by Optimod 13 64 November 7 2014 eek ee PRP AS versat e rigorous grating 0 ver Another of the Central Control Board 1s the lil interface Tt is nera to present the results if the Single Files option was chosen for output In order to view the results in the graphical window you first have to select which data to present Here you need to click the ADD button see below Be ile s Remove 2 Dateien Diagram C Progranme lt 0 ptimad sLI nigi A esults interface rm L Pragramme sL ptimad sLI nigi Hesults interfacell l re After clicking a file selection dialog opens and you can select the result files of your choice A preselect ion for the file type 1 e reflection transmission TE TM Cross Pol or ellipsometry can be done by means by means of the file type drop down box xl Reflection Files Pre m ree rem me r K rmn Reflection Files ne rr rem me rmn Transmission Files Pte tra bee bem tre TE Pol Files re te ree tee Th Pol Files rm m Imm Er Cross Pol Files P rem rme tern tme j Ellipsometry Files rta rea tta ten Tee TOME After the file selection is made the file name will appear in the related list see above and the graphic can be started by clicking the DIAGR
9. Sinus Beside the corrugation of the layers the distances and if existent the material ID s are shown Note that there is now distance entrance for the uppermost interface because it would have no meaning S uperstrat Thickness o pum Direct Input Real Part 1 000 Imaginary Part 0 000 Edit Layers Grating Period 0 5 pm Number of Layers 2 Show L arrugatian nm istance nm Material Ch Laper Sinus 100 000 LM Laver Paluqon 100 000 00 000 Add Layer to o Move up Move down Copy Cut Paste Delete Substrat Thickness o pm Direct Input Real Pare 2 000 Imaginary Part 0 000 Comment Help Cancel Fig 15 Unigit Stack Editor for 1D stacks for C method 4 3 Stack Editor 2D This editor is devised to facilitate the assembling of the patterned multilayer stack for a two dimensional or crossed grating It is launched by clicking either the EDIT or NEW box in the central control board group field stack if the radio button 2D is specified in the central control board The basic dialog of this editor is shown below There are two essential differences compared to the 1D case First the period in y and the non orthogonality angle zeta have to be specified 1n addition to the grating period in x Note zeta has to be put to zero for the standard orthogonal cell Copyright by Optimod 23 64 November 7 2014 o a Pf n t AAA AA Second there are different layer types available in 2D The stack e
10. Transition Slicing Polygon Refractive Slicing Fourier Depending on the selected layer type the layer editor shows up appropriately In the 1D case there are 8 options available Copyright by Optimod 28 64 November 7 2014 RHREREXESEXEXREESIU ROABADRSAA AQADANA UI B A TS GH TT _ re ppa oo oe a m sanan SS RAR Thin Film Rayleigh Fourier Polygonal Layer Rayleigh Fourier Sinus Layer RCWA Slice Hard Transition RCWA Slice Soft Transition Composite Layer Slicing Polygon Composite Layer Slicing Fourier Sequence 5 1 1 Flat Homogeneous Layer If the intention is to insert a flat homogeneous layer thin film the only thing left to do is to specify the thickness of the layer it has to be entered in microns and to the refractive index by means of the refraction index editor Moreover a name can be attached to the layer An example is shown in Fig 21 LT xi Name Layer Layer Type Thin Film Thickness 0 2 pm Refractive Index Medium 1 Direct Input Real Part 1 500 Imaginary Part 0 000 jsp cens eee Fig 21 Layer editor for 1D thin film layers 5 1 2 RF Polygon Layer This type of layer as well as the RF Sinus layer 1s backed by the so called Rayleigh Fourier approach The input scheme of the layer editor is depicted in Fig 22 Copyright by Optimod 29 64 November 7 2014 LI IEEDEPDITITIIIT FH eFIEI FEFH EHH ror 9
11. are several feasibilities to assemble the stack First new layers can be inserted by starting the layer editor clicking the INSERT button Second an existing layer can be edited by clicking the EDIT button This action also launches the layer editor with the selected layer In order to select a layer the cursor has to be positioned at the beginning of the associate description line Third the order can be changed by moving a marked layer up or down Fourth a layer can be deleted by marking it and press the DELETE button Moreover there are additional options coming with version 2 X X XX Layers can be marked by clicking with the left mouse button and concurrently holding the CTRL or SHIFT key and saved as a sequence file The marked layers must not necessarily form a coherent string 1 e unmarked lines are permitted between marked lines Copyright by Optimod 21 64 November 7 2014 i HERD versatile rigorous grating solver n Marked mem can wm copied or cut and later pasted this 1s also possible between different stacks for the information 1s stored to the clipboard For instance HL high low index quarter wave stacks can be built in this way Basically a multilayer comprises an arbitrary number of different layers embedded between substrate and superstrat For ID line gratings there are 5 basic types of layers homogeneous flat layer type 1 sinusoidal Rayleigh Fourier layer type 2 polygonal Rayleigh Fourie
12. cases are discussed in 10 Unigit consists of a Graphical User Interface GUI and four computation kernels The computation kernels are e unigit ID exe A solver for one dimensional 1D or line space gratings with orthogonal and or slanted layers in classical mount based on RCWA and Rayleigh Fourier method e unigit C exe A solver for one dimensional gratings in classical mount based on the C method e unigit co exe A solver for one dimensional 1D or line space gratings with orthogonal and or slanted layers in conical mount based on RCWA e unigit 2D exe A solver for non orthogonal crossed 2D gratings The four computation kernels can be utilized without the Unigit GUI by embedding it in user applications This can be done for example with Matlab Visual Basic C or CF In order to speed up the computation Unigit enables the parallel threading of loops This feature is particularly recommended to run slow 2D computations on multi core machines For instance a speed up factor of about 4 6 will become possible for a dual quad core machine The parallel threading can be activated via the pull down menu of the central control board for more details see section Fehler Verweisquelle konnte nicht gefunden werden Moreover the simulation of symmetric gratings illuminated in a symmetric setup may be accelerated by taking advantage of these symmetries see section 2 2 The related acceleration is about 3x theoretically 4x f
13. for 1D and 2D The difference is that a 1D sequence can only contain 1D layer types whereas a 2D sequence has to contain 2D layer types only However the appearance of the layer editor will be the same Basically a sequence can only be used if defined before This can be done in the stack editor or it 1s automatically done for the 1D slicing layers If a sequence layer is to be built into a stack the location of the stored file has to be specified in the corresponding edit field In addition the total thickness of the sequence has to be entered The structure of the sequence or sub stack is renormalized to this thickness Likewise the lateral dimensions are renormalized to the new pitch grating period The button EDIT permits to edit the sequence in the stack editor whereas the button Notepad opens a notepad with the sequence in ASCII format Copyright by Optimod 50 64 November 7 2014 x LER ELE Ed s o b EZELEZLELLARLAE NIGET ZIEIPIPITITI UTVXERBRBEBMRER AIIPIE I PTuEWwERMPERZRT 6 Refraction Index Editor This editor serves to define the refraction indices of all materials needed to build the layer stack 1 e the substrate the superstrat and all kinds of layers between It is available wherever required within the stack editor To call the editor one has simply to click the related EDIT button Related to the three basic possibilities of describing the materials the appearance of the editor changes correspondi
14. one dimensional stack files for the C method Copyright by Optimod 9 64 November 7 2014 TA T Serre T m z H rT versatil le rigorous b grating solver Pa o projection into the x y plane parallel to the y axis i e for an incident azimuthal andis of 90 degrees In order to activate the symmetry ae On the checkbox Sym has to be checked The user has to make sure that the selected grating is symmetric Otherwise wrong computation output will result CI ETT I Firm LII En t 1D Classic C 1D C Method C 1B Conical via s Save Result in A e a C Program Files OPTIMOD Fig 7 Selecting the Lalanne approach for 2D computations The appropriate solution kernel 1D 1C or 2D is checked automatically when a stack file is selected Furthermore Unigit detects automatically whether the correct solver routine is chosen and issues an error message 1f this not the case While the symmetry usage 1s an exact approach that requires a symmetric setup the smart order truncation is applicable to all 2D gratings It is automized and all the user has to do is to move the accuracy speed slider at the bottom of the CCB The default 1s the value 1 0 or left position of the slider It corresponds to standard 2D RCWA as known from publications Moving the slider to the right increases the speed but may reduce the accuracy Values between 4 and 8 not beyond are recommended but it may differ from cas
15. AM button The example for the dielectric interface 1s shown in Fig 11 Copyright by Optimod 14 64 November 7 2014 E Unigit PA m URCOMTEC c cn ce A E E m E LLI c ec pem T m LL Ca MEM Sitar ee 0 0 20 40 AO Degrees Axes Font Curves M Legend AutoScale min max size 15 1 E Label rr ToClipboard x AOI Degrees m 10 E Iw Connect Points Red Delete Cancel y Diffraction Efficien H o 1 0199 Arial Pensze moMarker Update Fig 11 Unigit diagram plot of computation results Unigit version 2 01 02 upwards features a new diagram tool provided by UrcomTech Berlin Germany It is based on an activeX library and has to be registered before usage The implemented diagram tool offers the following options to modify the plot e Switching the legend on off by checking unchecking the associated box e Autoscale the diagram to min max range by checking unchecking the associated box e Scale the diagram by entering min max values for x and y axes group e Change the font type and size font group e Select the active curve number by means of the up down arrows curves group e Change the label name of the active curve by entering the new name into the label edit field and push the Update button e Change the color of the active curver by means of the color selector e Change the marker type of the active curver by means of the marker type selector e Ch
16. AProgramme 0 phim x1 y x2 fo 00 o 300 fo 50 o2 20 i i Insert Replace Delete Edit Refractive Index mm gam 0730 1000 E Cancel Fig 36 Layer editor for a 2D patch filling layer The rectangles are specified by 2 diagonal corner points x1 y1 and x2 y2 and its material entry by means of the refraction index editor The embedding material is medium 1 Note that unlike the super ellipse layer there is no orthogonal option 1 e the patch is always defined in the given coordinate system This means in other words that patches which have been defined in a non orthogonal system pitch angle different from 0 are parallelograms in the real world Copyright by Optimod 42 64 November 7 2014 EEFFEPERPEDRE EZBERELEBRAE o UM gt TITIT me ma 5 3 3 Ellipse Layer Contrary to the patch layer type where a number of different areas can be specified the super ellipse layer type can include only one feature However this feature 1s a less restricted one namely a super ellipse The mathematical expression for a super ellipse 1s given below xy j DICE dx dy The appearance of the layer editor for an ellipse is shown in Fig 37 UNIGIT Layer Editor Mame Ino name Layer Type Ellipse_2D Thickness i um Refractive Index Medium 1 Direct Input Real Park 1 000 Imaginary Part 0 000 Refractive Index Medium 2 Ellipse Direct Input Real Part 7 500 Imagi
17. Doi Nr of hom fn IP L Delta 0 02 Deltaz 0 02 Slicing Fil Icin IE E EN ERI OK Fig 31 Input of a distorted re entrant profile by means of the 1D slicing Fourier layer The associated sliced profile 1s shown in Fig 32 SII z veri as x pon 1 0 3000 0 0000 1 0000 0 0000 00 0 6000 0 400 0200 0 3 0 0000 1 0000 0 0000 mm Insert Replace Delete c Moin 1 000 Mr of Paints 30 xo Deltas 0 03 Delta o Us Slicing File C Programme O ptimod Unigit Stacks seq seq ee Lancel Fig 32 Sliced profile of Fig 31 Eventually discrete interface points that are equidistant along the profile are generated from the Fourier series The total number of these points has to be specified in the input field Nr of points 5 1 8 Sequence The layer type sequence like a thin film layer is common for both 1D as well as 2D Therefore the editor appearance will also be the same It is depicted below Basically a sequence can only be used if defined before This can be done in the stack editor or it 1s automatically done for the 1D slicing layers If a sequence layer is to be built into a stack the location of the stored file has to be specified in the corresponding edit field In addition the total thickness of the sequence has to be entered The structure of the sequence or sub stack 1s renormalized to this thickness Likewise the lateral dimensions are renormalized to the new pitch
18. G Raoult A new theoretical method for diffraction ratings and its numerical application J Opt Paris 11 235 241 1980 9 L Li J Chandezon G Granet and J P Plumey Rigorous and efficient grating analysis method made easy for optical engineers Appl Opt 38 304 313 1999 10 J Bischoff Improved diffraction computation with a hybrid C RCWA method Proc SPIE 7272 part 2 2009 See e g http www osires biz page6 php reference 5 Copyright by Optimod 63 64 November 7 2014 AOI AR BARC CCB CD CM GUI PR RCWA RF TE TM ID 2D 3D Copyright by Optimod 64 64 Acronyms Angle of Incidence Anti Reflective Bottom Anti Reflective Coating Central Control Board Critical Dimension Coordinate Transformation Method a k a C method Graphical User Interface Photo resist Rigorous Coupled Wave Approach Rayleigh Fourier Method Transverse Electrical Transverse Magnetical one dimensional two dimensional three dimensional November 7 2014
19. HS HH Esa ali A o RT i RBAR 7 TT TT Ty a 7 Sanne ann aan e ann TT a BAL IM HARSAGRORGAS TT Senenenenan H M NN SC gt Fe rigorous o SON EE E NA EE inni UNIGIT me Editor Mame no name Layer Type Ellipse_2D Thickness f pum Refractiwe Index Medium 1 Direct Input Real Park 1 000 Imaginary Part 0 000 Refractive Index Medium 2 Ellipse Direct Input Real Part 7 500 Imaginar Part 0 000 Edit Refractive Index Medium 3 Ellipse 2 TS File Location D Program Filessaptimad sunigir amp NED atasalu nk Edit jw 2 Ellipse Same nk for Ellipse Resolution 256 x 256 0200 Power bic HQ gt a Be e a ES 5 3 4 Arbitrary Filling Unigit version 1 02 02 offers a new feature for arbitrary pixel filling of a 2D layer It is comparable to the gradient RCWA or soft slice in 1D If you want to include a arbitrary fill layer then pick the Fill2D option in the drop down box of the 2D layer editor Then the layer editor opens with the window shown in Fig 38 Copyright by Optimod 46 64 November 7 2014 mem T Layer Editor Mame arbitrary fil Layer Type Fitzb Thickness fi um Refractive Index Medium 1 Direct Input Real Part 1 000 Imaginar Part 0 000 File with 20 Fill information C Programme Optinod Unigit Stacks test Fed MotePad Fig 38 Layer editor for a 2D arbitrary filling layer Here you need to specify the layer thickne
20. M MM EMMERICH MEI COSE 4 PEE Ca ao CDO AA E stanley Gee ennststusiecineesco 5 Zea Moda ay RO MK e E E 5 2 2 COMPUTAUION P rebat at ri iii 7 2 3 Calculation of the Diffraction Angles cccccccnooonnccnnnnnccnnoconnnccnnnccnnnonnonacoconaccnnns 11 P A mom 12 2295 Re U Pe Set O ys areoe erste sect ssncecnnceesergecteous aoc dea see e E eR R M EPROSDEEN eS DEPONERE 13 A E E 16 Dads HOE a E E E E EE 16 Da UA 16 55 PO E ee E o RO ee eee 17 Je 6 10162 Be clanes NT ne ne ee 18 SEE Parel E OUR 18 ls SUO qt 19 DO Cross Section Viewer SelM OS acaecidos 19 A o 20 O IPIE 20 LEN A A seta dhennee sessnes aban esas 21 Aale cc disi P 2 LEE ssim MO T 22 E doulgpp 23 de RUINA 24 Zo A II HI SORS UC Ca A 25 A UTER 28 5 1 Layer Editor ID RCWA amp Rayleigh Fourier esses 28 5 1 1 Flat Homogeneous May m 29 241 2 AAPP O E MU 29 S43 Raylereh Fourier Simus Layer necia ia 31 5 1 4 RCWA Slice hard transition eese enemies 3l 5 1 5 RCWA Slice soft transition eeeeseeeeeeeeen eene nennen nnne nis 34 5 1 6 Composite Polygon Layer slicing sess 35 ll Composite Fourier Layer CS DITS estra n cos reU pun E 36 9 156 Ege A nidi te Tree are eee Roane be Ue dead ideis 38 s o MOM Ern AAA e o NI 39 SN C NERO O AAA Pen A 39 SANE UCET E eo 40
21. XD cdi 2D ROWA A tees 4 Dale Flat Homog ncous Id E ue ina ota ranita on E OU dio 42 oz BatenRectancle LaS aii 42 A o o 43 ode ADIOS ELIAS iio 46 3233 Composte 2D aay CIS OT 49 IO CCU c e e O easasaessaedenisoraunteeogecnneuenntesesesacie sexs 50 Oy ANG ira Chon Index EMO 51 Copyright by Optimod 3 64 November 7 2014 7 1 Ls Projecte Sener TT mU NEUES 58 Tee PEROIGCETOIPIC VIL TOC RR O En CO O oU SOne D rPUO ecd Tbe CN EIU UE 50 CN E E E N E U POE E S 60 Sl CER CMA 9 iii ese seneun see 60 5 2 Retnuevine mput IN TOMAN otr atole 61 8 3 Retrieving stack grating information cccoooooonnnnnnnnnnnnnnnnnonnnnnnnnnnonnnannnnnnnnnnnnnnnnannnnnss 61 8 4 Retrieving computation results occcccnonononnnncnnnnnnnononnnonnnnnnnnnnonononnnnnnnnnnnnnnnnnnnnnnss 62 BMC FNC oe COMI ado ERI eEMM UIN 63 PRC TOMY TING RERO 64 1 Introduction Unigit is a rigorous diffraction solver for 2D 1D periodic or 3D 2D periodic multilayer stacks see Fig 1 It runs on PC with Windows NT Windows 2000 Windows XP Vista and Windows 7 both 32 and 64 bit machines The schema in Fig 1 gives an idea what types of complex patterns can be solved with Unigit Superstrat 0 RCWA Slicing y PRENNE ec ais E in A p AAA cm A Enhanced Eu j e Rayleigh Fourier Thin Film ME ERCWA Slice Gradient Substrate Fig 1 Schematic representation of a multilayer stack Unigit V2 XX XX comprises three basic solution algor
22. aARAY YVAE URTA BSAA AMARA 5 SARREN i 520255 cc rie ANS e MOVE DOWN CTR V cursor down e COPY CTR C e CUT CTR X e PASTE CTR V e DELETE Delete key e SAVESEQUENCE CTR S 4 5 Cross Section Viewer In order to show the multi layer grating as a whole Unigit offers a new feature called cross section viewer The cross section viewer can be started after having loaded or created a valid stack file from within the stack editor by clicking the SHOW button see Fig 17 Currently it is only available for 1D gratings S uperstrat Thickness o im Direct Input Real Part 7 000 Imaginary Part 0 000 Layers Grating Period x 0 5 um Number of Layers 5 q mer Thick ness nm Material Slicing Fourier 150 000 Thin Film 100 000 ACWi 5lice Hard Transition 1000 000 Thin Film 100 000 Thin Film 250 000 Thin Film 100 000 Add Layer Edit Move up Move down Copy Cut Paste Delete Seq Savel Substrat Thickness lo pm File Location C SO ptimod LU nmigiSinsball MED ata alu nk Comment Help KMN Cancel wj Fig 17 Stack Editor with Show button starts the cross section viewer It works both for RCWA as well as C method gratings Some examples are shown below Copyright by Optimod 25 64 November 7 2014 e hn oe T ETE tee t y E t ro t 4 rtre e e a e j ARABE 000000 00000098
23. al investigations When you are finished entering the specification you need to click the button Calculate Slicing or the button OK to run the slicer module The result sliced profile is stored to the location contained in the editing field File Location make sure you have filled this field in order to avoid an error message By choosing the first option the window stays open and the button Show Sliced Profile becomes active Then the sliced profile can be visualised just by clicking this button with a result similar to what 1s shown in Fig 29 UNIGIT Layer Editor E xj M ame Polygon Laper Type Slicing Polygon Thickness 0 22 pum Refractiwe Index Medium 1 Direct Input Real Part 1 000 Imaginary Part 0 000 Edit Retraction Index Medium 2 Direct Input Real Park 2 000 Imaginary Part 0 000 Ealculate Slicing Show Sliced Profile Polygon Points relative Selig iz verras xs 1000 0 0000 0 0000 0 2500 0 000 0 7500 0 000 1 0000 0 0000 El z lo o O a Remove xo n Deka 0 02 Dekaz 0 02 ES File C Programme Cptimod Unigit Stacks seq seq zl 2 Cancel OK Fig 29 Presentation of the sliced profile in 1D composite polygon layer _ Inset Replace 5 1 7 Composite Fourier Layer slicing In principal the composite polygon layer is sufficient to specify all kinds of interfaces by applying an appropriate dense series of points With concern to curved surfaces this
24. ange the pen size of the active curver by means of the pen size selector e Delete the active curve by means of the Delete button e Connect Disconnect curve points by checking unchecking the Connect Points box e Note all changes in the curves group have to be activated by means of the Update button e Save the graph to the clippboard for further use Copyright by Optimod 15 64 November 7 2014 oes to 2 6 e 9 e 9 e LIIS Hag ahe Hin Ha E vg a IT Gams Gr zi E s EL E E E E is 2 a Aaa Short Cut LT DA E is G MA L An important extension of UNIGIT version 2 01 01 upwards is the introduction of UNIGIT projects file extension upr When activated in the output editor see 5 2 the complete input and result information of a UNIGIT run is stored in the project file Later all information can be restored from this file What s more all kind of results related to the application case can be generated from it with few exceptions saving time consuming reruns For a detailed description it 1s referred to section 8 of this manual Lal Hot Keys For faster access there are two hotkeys implemented in the CCB e SELECT STACK CTR S e EDIT STACK CTR E e OUTPUT EDITOR CTR O e NEW STACK CTR N e DIAGRAM TOOL CTR D e ADD FILE 2 Diagram CTR A e SELECT RESULT FILE CTR R e SEITINGS EDITOR CTR P e CANCEL UNIGIT CTR BREAK e EXIT UNIGIT CTR X e RUN ALT R 2 8 Pul
25. as opposed to it now he defines a real 3D body The vertical shape of this body 1s defined by the vertical power Here the 1 results in a straight line while a value gt 1 gives a convex and a value 1 results in a concave shape respectively Furthermore the user can define the number of slices Actually a equidistant slicing routine takes care to automatically translate the compact 3D description in something digestible for the RCWA solver Finally the user can sweep up and down through the 3D body by means of the Show Slice option Here the cross section shape of the activated slice number is plotted Fig 42 shows such a sequence of cross sections for the body defined above q i i pica r gt LI i L i LI c Lecce i i i i i i i i D i i Lud LA end Demum EI Led LENT ers A APA Im EA kv i i LI i i i i i 1 i i L i oo ee ee o Aww mene A AA Awww ee www wm ww we ele ew eee Aww ee wee 0280 050 07 0280 0590 0790 a 0259 0599 0790 E 02590 0590 09 yn Slice Top a jm Slice 4 m Slice 2 a jm Slice Bottom l Fig 42 Sequence of cross sections when vertically sweeping through a 2D composite layer 5 3 6 Sequence 2D The layer type sequence like a thin film layer is common
26. atically filled in by clicking the GET gt Conce x PROPAGATIVE ORDERS button e Eventually the complete diffraction matrices for reflection and or transmission can be output by checking the corresponding check boxes and determine the location to where to save the data 2 Eder aho TE The figure shows the example where the C Programme Optimod Unigit Results T est test A reflection matrix for TE polarisation is saved the folder Unigit Results Test test RTE Filename R Matrix TM eee E This matrix can be used for further computations such as the convolution with L Get Propagative Orders Filename T Matrix TE the angular plane wave spectrum of an E incident beam resulting in the diffracted Pame MSIE EM angular spectrum after passing the grating l 64 November 7 2014 Please note TET in 1 the case of conical diffraction the eoa o does not TE and therefore the diffraction matrices comprise all four polarisation combinations In this case only a reflection and or transmission matrix can be selected for output see below V Filename R Matrix 8 Filename H Matrix TM Filename T Matrix Filename T Matrix TM l Finally you need to check the Show Info in DOS window in order to display some auxiliary information during computation If you check this box the DOS window will get the focus otherwise it will remain in the background A context sensitive help for the output editor can
27. ation of the interface corresponding to the height of the profile and for the materials at either side of the interface see refraction index editor in section 6 In addition the distance to the next interface above has to be specified Due to the specifics of the C method there are no overhanging or undercut features allowed see 8 9 The material between the shown profile and the profile above is verified in the refractive index medium entrance Copyright by Optimod 39 64 November 7 2014 ARANA O MIA ATINA LLLLLILLJ Pri LESS IL IAQADADNANADNADANAN Yi a ABADADASAGAnAn EES Wty LJ ANA A A NANAA ALL a Oy E i w versati le rigorous grating s so ver m s Lll Mame lower Layer Type CCM_Polygon Distance 0 2 um Refractive Index Medium 1 Direct Input Real Part 1 500 Imaginary Part 0 010 Polygon Points relative m 0 000 0 000 0 250 0500 0750 1 000 Insert Replace Delete Corugation 0 1 pm E Cancel Fig 34 Layer editor for a 1D CM polygon layer to be run with C method 5 2 2 CM Sinusoidal Layer The layer editor for the CM polygonal layer is shown in Fig 35 It is very similar to the RF sinusoidal layer 1 e there entrances for the amplitude thickness of the layer the lateral phase XO and the relative strength of the second harmonic HR In addition the lateral phase x1 of the second harmonic can also be specified In general there would also be an entrance
28. be accessed by means of the button Note the same applies to all other locations of the software 1 e 1t will always directly jump to the relevant content of the help by hitting the help button After confirming with the OK button the output control data are saved to the output ctr file Basically it is possible to load output control files with different name In this way one can create a library of output control files for different standard situations 7 2 Project file generation In order to store all input information as well as the complete result information generated during a UNIGIT run except the memory consuming diffraction matrices the checkbox Project File has to be activated and a destination has to be entered where to save to the file see Fig 49 It receives automatically the extension upr to be clearly identified as UNIGIT Project File The file format is ASCII The information is stored in three consecutive blocks The first block contains the input comprising wavelengths AOI order truncation and polarisation It is followed by the grating or stack information Finally the results are stored as complex amplitudes for all propagative orders and all cases according to the loop specification Read more about the UNIGIT project handling and its features in section Copyright by Optimod 58 64 November 7 2014 EEEH E TIE 5 i FAA ES LECLLTELELER sens t i nada TIT Tr aN aaa EN
29. composite Fourier layer a k a slicing Fourier In the above example a sinus along with the first two odd harmonics k 3 and k 5 was input The waves have the amplitudes ZA 1 ZA 0 5 and ZA 0 25 The waves are not offset 1 e ZP 0 Moreover there is no distortion 1 e XA 0 Basically the input table has to be filled from k 0 thru the highest relevant order that means the highest order for which XA is different from zero This has to be obeyed even in the case that some orders here 2 and 4 disappear in this case ZA 0 has to be set In order to delete an entry click on the last number of the first column which activates the DELETE button Then just click the DELETE button Note only the last entry can be deleted Similar applies for the replacement of entry lines However here arbitrary lines can be replaced The information from an entry line is copied into the edit boxes by double clicking the number of this line Distortion can be implemented by means of adjusting the XA and XP properly An example of a distorted sine wave is shown below Depending on the XA values profiles with strong undercuts can be modeled see Fig 31 Copyright by Optimod 37 64 November 7 2014 i cadena b jssassaa TET mco e B a mmu BE versatile rigorous grating solvet UH Hm Layer verses xs 1 0 3000 0 0000 1 0000 0 0000 lo S000 jo 0000 i DO lo 0000 0 500 0 750 1 60 _ Insert
30. cores However the entered value can be different It is recommended to find an optimum number to achieve maximum computation speed by means of numerical experiments The default value for the delay time 1s 50 ms It is recommended to increase this value if synchronization issues occur 1 e single process threads fail 3 2 Color Table The color tab settings are closely linked to the color coding of materials and n amp k files In the second group box of the general settings called Color Code a color table file can be loaded and edited The color table itself is a simple Asci1 file that contains a list with pairs of color ID s names and assigned RGB color reference values The table can either be edited by Notepad or another Ascii editor or by means of the built in color table editor which can be called via the EDIT button see Fig 13 Material ID Alu Color Code gt pm Scroll Table Current Total Cancel Bz Fig 13 Color Table Editor The color table editor enables the viewing changing and adding of color assignments In order to add an entrance fill the material ID edit window with a new name of your choice and select a color by clicking the down arrow next to the color code Finally append the new pair by clicking the ADD button or discard your choice by doing anything else After adding a new pair the total score will be increased by 1 Currently the elimination of an entrance 1s only possible via th
31. cription is devoted to the regular mode The project retrieval mode 1s described in more detail in section 8 Copyright by Optimod 6 64 November 7 2014 2 2 Computation Preparation An essential function of the central control board 1s to determine the excitation conditions for the diffraction calculation Especially the following parameters may be defined The wavelength to be entered in microns The truncation number 1 e the minimum and maximum Rayleigh order to be kept in the diffraction matrix algorithm The polar incidence angle and The azimuthal incidence angle This option is activated only in the conical and 2D case A loop option 1s linked to each of these four parameters This means that the computation will be performed for several values of this parameter defined by a start stop and step value Optionally one geometry parameter of the stack may be also integrated in the loop selection In order to do this the particular parameter has to be indicated by means of a dollar sign at the end of its line 1n the stack file You can do this by opening the file with the notepad button The example in Fig 3 shows the selection of the grating thickness as a parameter dielgrat_1d txt Editor AE Datei Bearbeiten Format Ansicht dD Stack 1 000000 Gitterperiode z in um T Anzahl der schichten 0 Direct Input 1 000000 0 000000 Refraction Index O 000000 ff Dicke Superstr at ditt 0 Direct I
32. ct TET H AMAN T T THES samnnnn isl x Datel Bearbeiten Format Ansicht kolor Alu 136 427 67 165 634 198 524 886 291 747 263 854 535 329 268 395 047 F12 982 494 994 4 A 5 5 6 6 6 7 T 8 8 9 a 1 PRRPRPRPRPRRPB SI un un WW Lu NM ES 097 KE n kE E C C L2 H2 ES lS OB S LS D D CO CO CO CO CO CO o o o Co C C C C c mom mom cmcmmmmmmcooononooooooncoccm ccm Pa d Fig 46 n amp k file listing with material ID for color coding indicated by key word color Moreover the refractive index can be defined by means of a certain dispersion formula Then the input mask looks like shown in Fig 47 Substrat Index Editor Cauchy Select nifi na 0 2 n3 0 1 Delete Save Cancel Fig 47 Refraction input via dispersion formula Depending on the selected dispersion formula the coefficients n1 thru n3 4 or 5 as required by the related dispersion formula have to be entered Make sure that the coefficients are related to the wavelength as given in microns rather than nanometer Angstrom or other length measures Another possibility 1s to select a certain coefficient set from the combination field In addition once the coefficients are entered the present coefficient set can be saved In order to be able to recall the set properly a name has to be entered in the select box Then it 1s available under this name for future operations
33. ditor for a 2D grating is shown in Fig 16 UNIGIT Stack Editor x Superstrat Thickness 0 um Direct Input Real Part 1 000 Imaginary Part 0 000 Edit Layers Grating Period x 10 5 um y 0 5 um zeta fo degrees Number of Layers 5 No Thickness nm Thin film 1 Thin Film 100 000 W Patch 2 Patch 200 000 Ellipse 3 Ellipse 300 000 ZA Arbitrary Fill 4 Fill2D 400 000 SO Sequence 5 Sequence 500 000 Edit Move up Move down Copy Cut Paste Delete Seq Save Substrat Thickness pm Direct Input Real Part 1 500 Imaginary Part 0 000 Edit pi Comment Cancel Eea OK Fig 16 Unigit Stack Editor for 2D stacks For 2D crossed gratings there are 4 basic types of layers homogeneous flat layer a k a thin film type 1 patch rectangle layer type 2 Super Ellipse layer type 3 Arbitrary fill layer type 4 Like in 1D sequence layers can be build An example of the stack editor 1s shown in the figure above Rayleigh Fourier layers are not available for the 2D case However there is an option available to describe 2D composite layers 1 e real 3D structures This can be achieved via the CONE_3D option in the layer editor see section 5 3 5 4 4 Hot keys There are some hotkeys available in the stack editor to make life easier namely e ADD LAYER CTR A e EDIT LAYER CTR E e MOVE UP CTR T cursor up Copyright by Optimod 24 64 November 7 2014 LE URT S12 123 eS AamauM
34. e Notepad editor 3 3 Cross Section Viewer Settings While the colors of the cross section view are controlled by the color table in conjunction with the n amp k settings the overall appearance can be controlled by the settings 1n the cross section viewer group box There are three settings The substrate height defines the relative height of the substrate shown in the plot in relation to the total stack height Similarly the superstrat height defines its relative height however since the superstrat is not color coded it is just the relation of the unfilled area above the grating Eventually the check box Show recessed stack enables to recess the stack relative to the substrate Copyright by Optimod 19 64 November 7 2014 iun de o tod t a ae i c sake n Lr as a i ILELELELE 3 4 Stack File Settings The only one setting of this group box gives the user the choice how to proceed after editing and rename the active stack file Previously Unigit has kept the old file as active file the one that 1s run when hitting the start button Because this has lead to some misunderstanding the user has now the option to decide whether or not to have the new edited stack file as active file The default setting 1s to use the new file box 1s checked 3 5 Python Settings Unigit offers the possibility to run Python scripts directly from the CCB see section 2 9 The active python script file can be loaded and edit
35. e RF a solution is obtained in one single step by the application of the Rayleigh Fourier method a composite layer is first sliced into elementary RCWA slices that are solved separately In addition to polygonal profile specification a trapezoid profile can be seen in the 1mage example there are two input parameter that control the slicing process namely DeltaX and Copyright by Optimod 35 64 November 7 2014 o NEEHHUNU i DeltaZ While the former defines the relative maximum step from one slice to the next one in lateral direction the latter regulates the slicing process near maxima with very smooth slopes Clearly these slicing parameters may have a strong impact on the diffraction computation results Keeping the lateral step width constant results in slice thicknesses of the individual RCWA slices indirectly proportional to the local slope of the profile to be sliced Generally the necessary quantization 1s determined by various factors such as the aspect ratio the wavelength to corrugation ratio the profile shape the refractive indices etc As a rule of the thumb a slicing criteria postulates that the absolute step width 1 e DeltaX multiplied by the grating period should be less than about a tenth to a twentieth of a wavelength On the one hand a finer slicing means increased accuracy of the computations On the other hand the computation time is increased likewise An optimum value can be ascertained by means of numeric
36. e set as active stack file and the basic operation mode of Unigit can be switched back to regular by clicking the SET STACK button Concurrently Copyright by Optimod 61 64 November 7 2014 Le TY Pee LE m TABABRUXPERT ELI EEUU n E55 O TX INANANACA ANANE Ada P ci NN i ipi IITIPIPITITI i y NAR ARANANAN 411113 azul TITETUDUTTY AGA FEREREERRT wae Unigit identifies whether the stack file is a valid Unigit format and issues an error message if this is not the case a 6 4 Retrieving computation results Another very important functionality of UNIGIT s project retrieval mode 1s the generation of arbitrary result information from a given project file This is simply done by clicking the EXTRACT RESULTS button The way how the output is organised has to be set in exactly the same way as for the regular mode Again this is done by means of the output editor see section 7 1 in exactly the same way as for the regular mode Actually you will see only subtle change in appearance when starting the output editor described elsewhere In addition some options will be disabled output only in one file Analogously either single files one for each diffraction order one big file all in one or no file meaning the output 1s displayed in a DOS window can be generated The essential difference 1s that the information is retrieved from a sort of archive UPR file instead of being generat
37. e to case the example below shows 7 84 Approximately these values correspond to the speed up An appropriate setting can be verified by means of an extented convergence analysis This means to run a regular 2D RCWA with very high order first and save the result as a reference Then several order convergence loops have to be run with different slider position e g 1 2 4 6 8 and 10 Finally all this results have to be related to the reference which 1s supposed to be the correct result resulting in a trade off order speed pair for a given accuracy Copyright by Optimod 10 64 November 7 2014 III IEUUUUu guuunoo ooo Q o X 3 1 Le ee es RAVAVANRY a oo f PALLES o te A ARNADARADROANANANO pter ree tert i n P 4 y i L Pur 5 L gt me 44 b EAVAVZA ALIIITIIIIRIISTISIAUA RARBAMN a HLLDEPRDERPRPHPHPRMPIMS SAGAHTUBOADADAE p LER TT 22 111 sss E asia mad unm o NENNEN is 4 eddie A d EE eee ae BS 11113131341 p BARY onene LELIIIIIIITITITI ED BNEOssl m fJc J J GG c s TTTTITITITITITTTTT TITO TT HOPED QL LI OGO O O 10 HPHPBFBE BLBEMMM tddi BARABAR RRNANARRR T ATT LCLTCITARTITTILILIT LLLLI SLLLCLLLLLLLLAA MLULLLCLLCLCLCLLLL Computation gt Result File s 1D Classic 1D C Method C 1D Conical La Accuracy 7 84 Speed Show Angles 2 3 Calculation o
38. ed by a solver Thus it is much faster Of course all onboard features for data exploration 1 e starting a notepad to display the ASCII formatted result files or the diagram feature can be applied the usual way see section 2 5 Copyright by Optimod 62 64 November 7 2014 References 1 M G Moharam D A Pommet and E B Grann Stable implementation of the rigorous coupled wave analysis for surface relief gratings enhanced transmittance matrix approach J Opt Soc Am A 12 1995 pp 1077 1086 2 Lifeng Li Multilayer modal method for diffraction gratings of arbitrary profile depth and permittivity J Opt Soc Am A 10 1993 pp 2581 2591 3 D Agassi and T F George Convergent schema for light scattering from an arbitrary deep metallic grating Phys Rev B 33 1986 pp 2393 2400 4 Lifeng Li Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings J Opt Soc Am A 13 1996 pp 1024 1035 5 Lifeng Li Use of Fourier series in the analysis of discontinuous periodic structures J Opt Soc Am A 13 1996 pp 1870 1876 6 Lifeng Li New formulation of the Fourier Modal Method for crossed surface relief gratings J Opt Soc Am A 14 1997 pp 2758 2767 7 P Lalanne Improved formulation of the coupled wave method for two dimensional gratings J Opt Soc Am A 14 1997 pp 1592 1598 8 J Chandezon D Maystre and
39. ed via the buttons LOAD and EDIT The Python editor that is called can be verified in the edit box next to the button Copyright by Optimod 20 64 November 7 2014 LEE LJ LA AT tte i s versati TO A a a a a EESAHARERR A A ES TL rig 4 Stack Editor 4 f Stack Editor 1D This editor is devised to facilitate the assembling of the patterned multilayer stack It 1s launched by clicking either the EDIT or NEW button in the central control board group field stack The basic dialog of this editor is shown in Fig 14 UNIGIT Stack Editor xi Superstrat Thickness lo um Direct Input Real Part 1 000 Imaginary Part 0 000 Edit Layers Grating Period x 1 um Number of Layers 8 No Thickness nm E Thin Film 1 Thin Film 100 000 RF Polygon 2 RF Layer Polygon 200 000 RF Sinus 3 RF Layer Sinus 300 000 IE RCw A Slice 4 RACWA Slice hard 400 000 MACWA Gradient 5 RCWA Slice gradient 500 000 FA Polygon slice 6 Slicing Polygon 600 000 FU wave slice 7 Slicing Fourier 700 000 S8 Sequence 8 Sequence 800 000 Edit Move up Move dowr Copy Cut Delete Seq Save Substrat Thickness lo pun Direct Input Real Part 1 500 Imaginary Part 0 000 E dit Comment Help Cancel OK n Fig 14 Unigit Stack Editor for 1D stacks The stack editor facilitates the assembling of arbitrary multilayer grating structures To this end a number of buttons are arranged below the spreadsheet list There
40. ellmeier coefficients required n1 n9 n k o fl UY ad C94 Copyright by Optimod 55 64 November 7 2014 TA T UHCECHCPM T m zs H E versatil le rigorous b grating solver i e Po o A 7 Output Editor 7 1 Basic features The output editor is started either by the EDIT button in the Output group of the Central Control Board It brings up the output editor window as shown in Fig 48 UNIGIT Output Editor Output Files Output Format Output Value t So Output File New File Float t 4 Digits f Efficiency Allin One Append O Fix C 8 Digits Efficiency amp Phase Single Files Sci t Amplitude amp Phase Phase t Efficiency total TanPsi CosDelta Iw Reflection iw Transmission Efficiencies in Filename A Matriz TE Ls Complex Value Filename R Matri TM Output Orders M y Filename T Matriz TE TES E m hd aximum 0 n Filename T Matrix TM SUUS L Get Propagative Orders Project File Show Info in DOS Window ja 7 Cancel Ok Fig 48 Output control editor Here the following choices can be made e selection where to write the output to radio buttons top left o No output file means the result appears in the DOS window o All in one means the result 1 e all selected diffraction orders are written into one file This file can be specified in the Central Control Board in the text box Save result in
41. er Editor x Name RF Sinus Layer Type RF Sinus Layer y Thickness 10 2 pum Refractive Index Medium 1 Direct Input Real Part 1 000 Imaginary Part 0 000 E dit Refractive Index Medium 2 File Location C Programme O ptimod Unigit NKD ata sag nk Laer iz uer as 6 wo A A bb b A a ecssbornolboso bo Fig 24 Layer editor for 1D RF Sinus layers Here the input procedure is the same for step 1 and 2 like in the RF polygon layer The profile is determined by the sinus function The lateral shift can be adjusted by means of the phase xO a value of 0 25 defines for example a negative cosine function 5 1 4 RCWA Slice hard transition Copyright by Optimod 31 64 November 7 2014 an 2814 eiii O Gh tin O Gn am 6 vers TIS e rigorous grating sol E E mi FEEHI T1 AAA CEA IS TE FH zin 1 nasapaAPAMAE Jn TT PRRRRRR RRR TD This alice type is a sort of TN work horse of the UNIGIT code In principal all TER p patterned multilayer stacks including all kinds of layers even inhomogeneous ones volume scatterers that are separated by all kinds of interfaces including of course undercut profiles can be constructed by means of it The related layer editor 1s shown in Fig 25 Marne nc name Layer Type RCwA Slice Hard Thickness 1 um Skew D deg Hi x Partitions normalized Numa Refraction Index Material ID Direct Input Real Pa
42. ettings can be accessed via Misc General Settings in the pull down menu of the CCB An example of the settings window is shown in Fig 12 Fig 12 General Settings Table 3 1 Parallel Editor The former parallel editor has been replaced by the new general settings in order to accommodate more controls for Unigit runs and presentations It can now be found as a group box named Parallel Loop on top of the settings window First of all the choice whether or not to take advantage of the parallel loop threading has to be done by checking or unchecking the check box Parallel Presently the parallel looping does not allow to output the computation results 1n single files ready to be used with the diagram Copyright by Optimod 18 64 November 7 2014 Tn Moreover it may Show w synchronization i ISSUES fail o of quem threads e g loop variables when Unigit project files are to be written In addition one should be aware that Unigit generates temporary files during parallel looping which are deleted afterwards So the simulation run may be vulnerable to conflicts with the file system issues caused by missing user privileges After activiation of the parallel looping mode two edit fields become active the number parallel threads and the delay time between the various thread launches An arbitrary integer number greater zero should be entered for the number of threads The default is the number of available computation
43. f the Diffraction Angles Basically Unigit offers two different options for the calculation of the diffraction angles The first quick option can be done upfront and does not need to run the RCWA or C method computation kernels It can be launched by clicking the button SHOW ANGLES The results are shown immediately in a Notepad window An example is inserted in Fig 8 for a dielectric grating Nsubstrate 1 5 with pitch 1 micron at 0 5 and AOI 45 Unigit Diff Angles txt Editor Datel Bearbeiten Format Ansicht Diffraction Angles pitch in microns AOI in degrees PHI in degrees index superstrat 12 457 180 000 031 180 000 053 0 000 transmission 1 500000 f index substrate Order Theta Phi 4 50 534 180 000 3 31 911 180 000 2 11 260 180 000 1 7 936 0 000 O 28 126 0 000 1 53 585 0 000 Fig 8 Presentation of diffraction angles In the second option the angular information is a by product of a full computation run In order to access it one has to generate an Unigit project file upr see section 7 2 In order to retrieve the angular information from the project file one has to reload the project file after the computation run has finished see section 7 3 and pick the diffraction angles option in the output editor see Fig 48 Copyright by Optimod 11 64 November 7 2014 The ia are are defined to Fig 9 The polar m 0 are measured eco the normal axis z and t
44. for the distance to the layer above This is not visible here since the interface shown in Fig 35 is the uppermost of the stack shown in Fig 15 For the same reason the index is set automatically to the superstrat index that is specified in the stack editor see section 4 Copyright by Optimod 40 64 November 7 2014 LA ANNIE A AAA Poe eosin 111111 Li 111 LLELLITA ani AROREACADIADA nan rr RRRANAR ARORAA N an LOLLLLLLLDTA TTL tite LiL PPPPPPT Mame sinus Layer Type LLM Sinus Refractive Indes set to nk_Superstrate 4 Q4 0 000 0 250 0 500 0 50 1 000 au 0 75 al lo HA lo Amplitude 01 pm p p BL 27 Lancel Fig 35 Layer editor for a 1D CM sinusoidal layer to be run with C method 5 3 Layer Editor 2D RCWA The layer editor can be activated from within the stack editor Its appearance and functionality depends on whether the 1D classical or conical or 2D option is selected If activated by the ADD LAYER button within the stack editor the layer editor will appear and offer the input of a thin film layer Another layer type can be picked by means of the drop down box as shown below UMIGIT Layer Editor Mame nc name Layer Type Thin Film Thickre Thin Film Patch Direct Input Alf Fill2D Sequence Refractive Depending on the selected layer type the 2D layer editor is opened In the 2D case there are 5 op
45. grating period The button EDIT permits to edit the sequence in the stack editor whereas the button Notepad opens a notepad with the sequence in ASCII format The layer editor window for a sequence 1s shown in Fig 33 Copyright by Optimod 38 64 November 7 2014 oo i Hu DTI FRAN AER nne Bra seriei Eussesseeas ALAMOS an ec o AE LLLI LS NAIRABANADAR ANMBARARARAD ALLLLLLLLOEES O Gh tin A E 6 le rigorous grating sol er UNIGIT IF Editor EE xj Mame example Layer Type Sequence Thickness um Sequence File EProgramme D ptimiad llnigi Stacks ssegl seq s E dit MotePad mg Cancel Fig 33 Layer editor for 1D sequence layers 5 2 Layer Editor 1C C method Likewise the layer editor to run the C method solver is activated from the stack editor by clicking either the button ADD_LAYER or highlighting one layer and clicking EDIT hotkey CTR E As opposed to the RCWA where the stack is assembled by layers such as slices or thin films the stack in the C method is rather described by interfaces its corrugations and distances to each other Therefore the term interface is mainly used in the following while layer if used is understood as a synonym for interface rather than a real layer 5 2 1 CM Polygon The layer editor for the CM polygonal layer or better interface 1s shown in Fig 34 It is very similar to the RF polygonal layer 1 e there entrances for the corrug
46. he incident or diffracted ray The azimuthal angles q are measured between the projection of the ray into the x y plane and the x axis 7 diffracted O 0 3 y incident Pa Fig 9 Definition of the incidence and diffraction angles in Unigit 2 4 Computation Run The computation is launched by clicking the START button below Before hitting the button make sure that the wanted stack file is selected complying with the computation mode 1D IC or 2D Otherwise an error message will occur During computation a DOS window appears which may show additional information about the state of numerical calculations The START button will be replaced by a progress indicator After having completed the task the START button appears again and the computation time is displayed above the button During computation the potes 1s shown instead of the START button see Fig 10 Computation 1D Classic Save Result in C 1D Conical C Programme Optimod Unic 2D La Delete File The computation time of the last run was 15 sec 25 done Cancel BEREEE Fig 10 The progress is shown during running a computation It is possible to stop the computation with the CANCEL button If you have checked the Show Info in DOS Window check box or the No output file radio button in the output editor a DOS window pops up during computation showing either intermediate auxiliary information or in the latter case the final results Co
47. iewer section 4 5 The input procedure for the slice 1s as follows Copyright by Optimod 32 64 November 7 2014 e ooo eo rerrrr a A A ee O ANN T T us E E vers sati le rigorous grating so eco To eee o ts te a APURAR BNAARARARAN LL oL TT e ect First enter the thickness of the slice 1n microns Second enter the skew angle in degrees default is 0 which relates to standard RE WA Third specify the partitions in the x partitions group field This 1s done by entering the lateral value of the right hand border of the partitions in the x input field and press either REPLACE in order to replace the marked partition or INSERT in order to insert the value it is sorted automatically into the existing list Notice that the x value input 1s relative 1 e between 0 and 1 The renormalization to the grating period is done automatically Furthermore if the biggest x value xmax is not equal to 1 the region from xmax through is filled with the same material like the left hand partition In other words the partition 1s completed across the period Third define the optical properties of the partitions by activating it 1 e clicking at the x value and the activated partition is highlighted in grey colour Then press the button EDIT REFRACTIVE INDEX to call the refraction index editor Unigit features a new enhanced RCWA solver that 1s able to directly solve slanted gratings thus avoidi
48. ipse descriptor ellipse filling e stack2d_arbi ust using the new bitmap descriptor arbitrary filling e stack2d rect ust using the patch descriptor patch or rectangle filling Running these files should give very similar results for details see Unigit tutorial 5 3 5 Composite 2D Layers This layer type permits to implement real 3D structures by means of a very compact description It is quite similar to the 1D composite layer types in the sense that an automatic slicing works behind the scenes to transform the input description in a number of 2D slices of the 2D ellipse layer type It is activated by selecting the CONE 3D option in the 2D layer editor In doing so the layer editor window as depicted in Fig 41 shows up UNIGIT Layer Editor Mame no name Layer Type Cone 3D Thickness f um Refractive Index Medium 1 Direct Input Real Park 1 000 Imaginary Part 0 000 Edit Refractive Index Medium 2 Ellipse Direct Input Real Part 7 000 Imaginary Part 0 000 Edit dx dy y Power Angle Power vertical E of Slices E E Shown Slice Bottom Slicing File a Resolution 256 x 256 y Iv Ortho Q000 02320 0300 0750 100 2 Cancel Fig 41 Unigit Layer Editor for 2D composite layers Copyright by Optimod 49 64 November 7 2014 Here the user can shine the top and the bottom cross section shape of his grating pattern just like the same way as he is used to with the ellipse filling feature But
49. ithms e the Rigorous Coupled Wave Approach RCWA a k a Modal Method with Fourier Expansion see e g 1 2 e the Chandezon method C method a k a Coordinate Transformation Method see e g 8 amp 9 e and the Rayleigh Fourier Method 3 which is not rigorous Presently algorithms one and three are embedded in the same S matrix algorithm see e g 4 ensuring a high degree of stability as well as flexibility while the C method is implemented separately It is planned however to merge all three algorithms into one frame for upcoming versions The algorithms can be applied layer wise 1 e one layer can be treated with Rayleigh Fourier and another layer with RCWA The implementation of RCWA was Copyright by Optimod 4 64 November 7 2014 eee versatile rigorous grating solver n done in T with Lifeng Li s factorization rules see e g 5 to insure accurate results The 2D algorithm follows closely Lifeng Li s paper 6 In addition it offers the choice of the Lalanne method 7 instead of the Li Method The implementation of the C method followed mainly the description in 9 as well as some sophisticated schemas to couple the fields between non parallel interfaces The C method is an ideal supplement to the RCWA Its preferred application cases are profiles with shallow slopes made from high contrast materials A particular case are Echelle gratings Some examples proving the superiority of the C method in these
50. l Down Menue In addition many functions can be accessed through the pull down menue of the CCB The following groups and functions are implemented File O OO 0 0 Edit O O Project O O O Misc O O O O Load Stack Load Output Result File New Stack File Exit Edit Stack File Edit Out Ctr Get Stack Set Stack Set Input Parallel Show Angles Add Curve Remove Curve Copyright by Optimod loads an existing stack file loads an existing output control file opens an explorer for entering the result file opens the stack editor to create a new stack file exits the Unigit program opens the stack editor to edit the selected stack file opens the output editor to edit the output control file retrieve the input information from a Unigit project file opens the parallel loop editor computes and displays the diffraction angles adds a result data set to be displayed as diagram removes a selected curve to be displayed as diagram 16 64 November 7 2014 o Diagram 2 9 Python Link Python scripts can be directly run from Unigit by clicking the PYTHON button to the left of the SHOW ANGLES button The Python script to be run can be selected in the general settings see section 3 5 Examples of Python scripts that show how to call Unigit are provided on request Copyright by Optimod 17 64 November 7 2014 pe Anananae aan T1 ID 3 General Settings The general s
51. l or 1D conical similar applies for 2D On the other hand C method based stack files can only be run by the 1C routine There are four solver routines available e 1D classical RCWA Rayleigh Fourier for line space gratings in classical mount 1 e azimuthal angle is equal to O and no polarization coupling occurs e IC classical C method for line space gratings in classical mount e 1D conical for line space gratings in conical mount where the azimuthal angle can be freely defined Here the polarization may couple between TE and TM and therefore the polarisations cannot be separated any more e 2D for crossed gratings These gratings are characterized by two spatial periods When the two periodic directions include a 90 degree angle it is called an orthogonal grating Otherwise the grating is called non orthogonal Furthermore the 2D grating can be run either according to Lifeng Li s algorithm 6 or based on Lalanne s approach 7 The selection is done by means of the checkbox La If checked the Lalanne approach is asking for an weighing factor factor a in equation 1b of 7 it has to be between 0 and 1 as shown in Fig 7 An additional way to accelerate 2D computations is to take advantage of inherent symmetries This means that both the stack as well as the excitation have to be symmetric Presently this feature 1s only implemented for a symmetric orthogonal grating illuminated by a beam having a There are only
52. lect whether to output efficiencies in per cent or related to 1 1 means 100 with the Efficiencies in checkbox o Select the way of number output Float Fix or Scientific o Select the number of digits 4 or 8 e Selection of the output values radio button group top right o Efficiency outputs diffraction efficiencies in or related to 1 see above o Efficiency amp Phase same as before plus the absolute phases o Amplitude amp Phase outputs the absolute value of the complex amplitude plus the absolute phase no efficiency correction o Phase outputs only the absolute phase o Efficiency total summarizes the efficiencies of both polarisations in the output channel e g TMM amp TEM o TanPsi CosDelta outputs the ellipsometry values only for zeroth order Note TanPsi is output as log value o Complex Value outputs real and imaginary value of the complex amplitude e Selection of the output orders here you can determine the Uutput Diets orders to be output The input has to be done in a from a m minimum order to Rid order manner In the Fm KE example shown in the output editor the 1 and the 0 order Maximum 0 are output for a 1D stack Another example for 2D is shown below Here the following order combinations are output 1 1 1 0 1 1 1 2 0 1 0 0 0 1 amp 0 42 Moreover Shows Info in DOS Window the propagative orders in reflection can be determined and autom
53. may be sometimes rather cumbersome To this end a definition of the profile in terms of parametric Copyright by Optimod 36 64 November 7 2014 TA T UHCECHCPM coo NEN FF n z a E E versatil le rigorous b grating solver iT A M 9779 G4r A9 9 hA5 S I rr ee he ne Le ma omia ne Fourier series was oE Here both the unm and the abscissa are given as a Fourier series of a parameter t as follows t gt XA sin 27kt XP k z t Y ZA sin 27kt ZP k Setting all coefficients XA to zero leads to the known Cartesian Fourier representation Instead of the direct input of the interface by means of point series the coefficients ZA and XAx as well as the phases ZP and XP have to be entered The related layer editor is shown in Fig 30 x Mame wave Layer Type Slicing Fourier Thickness 1 5 Lum Refractive Indes Medium 1 Direct Input Real Part 1 000 Imaginary Part 0 000 E dit Refractive Indes Medium 2 E l l m Calculate Slicing File Location EA Programme O ptimad sLl nigis H KD atasan nk A i Show Sliced Profile 0 0000 0 0000 17 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 1 2 3 O 0000 O 0000 0 5000 0 0000 4 A 0 0000 0 0000 0 2500 0 0000 fo 0000 nono fo25 fo 0000 anon 0330 0500 DT 12000 inset Replace Delete Nr of Paints 30 xojo Dieltax 002 Delaz 002 Fig 30 Layer editor for 1D
54. microns f Lambda Start o 81 End o B2 Step 0 005 r Rarlelgh Orderz Truncation 2 2 Incidence Angle polar Theta i Project Control r Incidenee Angle azimut Get Stack C Phi 0 4 H Set Input ack Project File C Program Files O ptimod Unigith Results MT_ auonsi upr Computation Result File s t 1D Classic t 1D C Method t 1D Canical f 2D La EN ES Accuracy 10 Speed gw Diemen a No File Selected Save Result in E Program FilesS OPTIMODSUNIGIT SAesults result Notepad Fig 51 Appearance of the central control board in project retrieval mode 8 2 Retrieving input information The input information is simply retrieved by clicking the button SET INPUT in the group Project Control Then all input masks such as Lambda Truncation Theta 1 and Phi 1 are updated with the original state used to generate the active project file Likewise the loop setting 1s updated along with the associated start stop and step parameters 8 3 Retrieving stack grating information The retrieval of the original stack information is a two step procedure In the first step the stack information is retrieved and saved to a file by means of the GET STACK button To this end a file name has to specified by means of the output editor see section 7 3 After successful operation the SET STACK button is enabled In the second step the stack file can b
55. nar Part 0 000 M E ooo q 4Q4 ERIT Resolution 2564 256 l Power Angle ps psf h 2 gt Foe IS Fig 37 Layer editor for a 2D ellipse filling layer The embedding medium is medium 1 and the ellipse is medium 2 The dx and dy are the diameter in x and y direction whereas sx and sy are the relative lateral shifts Angle is the rotation angle of the ellipse Unlike a regular ellipse with power p 2 the pem power p of a super ellipse can be an arbitrary oao positive rational number In this way a range of features between an ellipse and a rectangle p infinity can be covered Moreover a Resolution diamond can be described with p 1 and 2 z concave shapes with p lt 1 Two cases are Power Ange amo shown below fi fo 0sm 577 0 500 0730 12000 Copyright by Optimod 43 22 Cancel m EIrrrrrrrerrrrrr LH I H 0 o0 0 o0 9 m o i ite rigorous grating s so ver e A E HIE y g E E versa 7 rer x ETE auda andar ade nde nde m m mo m Moreover the ellipse can be rotated by specifying the wanted rotation angle and it can be shifted laterally by entering the correspond relative values into the edit fields sx and sy By checking or unchecking Ortho you can define whether or not the ellipse is orthogonal in real world in spite of a non orthogonal cell defined by zeta see stack 0 000 o Resoluti
56. ng the tantalizing and time consuming procedure of slicing What is more the skewness can be defined layer wise An example of a slanted grating is shown below in Fig Stack cross section Fig 26 Slanted grating the skew angle is measured between the vertical axis and the new non orthogonal axis which follows the slanted profile Copyright by Optimod 33 64 November 7 2014 PEEHERREHIES H AT RuBHRRREBAE AM MAMADA ev rr AARNAVRRAVEVAVANZA a 5 B 5 RCWA Slice soft transition The soft transition slice a k a gradient layer resembles widely the hard transition case However there 1s a distinct difference in the layer description While for the hard transition arbitrary values for the position and number of borders can be selected the partitions in the soft case have all the same widths and the number of partitions is restricted to a power of 2 e g 16 32 64 or 128 An example of the layer editor 1s shown in Fig 27 UNIGIT Layer Editor X Name Gradient layer Layer Type Thickness 0 05 pm Related File Ic Programme O ptimod Unigit Stacks test nar NotePad ES Cancel Fig 27 Layer editor for 1D gradient layer RCWA slice with soft transition Accordingly the input procedure is different First the thickness of the slice has to be entered Second the skewness angle has to be specified see section 5 1 4 Third the layer has to be specified The desc
57. ngly After being called it comes always up in the direct refraction index input mode as shown in Fig 43 Direct Input Material EY Real 2 Imaginar lo Color Code a 7 Cancel Fig 43 Refraction index editor Here the real and the imaginary part of the refraction can be inserted directly Then this values are taken for all related calculations no matter what wavelength was specified Apparently in this way no dispersion is taken into account Moreover a material ID can be assigned While entering an ID name Unigit checks the color table see section 3 2 for this name and if being found presents the color assigned to it Other selections can be straightforwardly made by choosing the wanted option in the drop down box This is shown in Fig 44 along with all the possible options Substrat Index Editor a xj Direct Input Direct Input Cancel Sellmeier Schott Fig 44 Selection of the refraction index input mode The available selections fall into three basic options e Beside the direct input one can e get the index information from a file Copyright by Optimod 51 64 November 7 2014 muuxS RR Hrtnnb e or have it emer from a certain dispersion fc formula Buchdahl Cauchy etc gt If you pick the file input the index editor will have the look depicted in Fig 43 Substrat Index Editor l x File Input bl File Location E n Cancel Fig 45 Refraction i
58. nput 1 500000 0 000000 Refraction Index O 000000 f f Dicke Substrat pirr 4 Af Ree HE bin HARE 2 Anzahl Bereiche Direct Input Q 1 000000 0 000000 Refraction Index O 500000 f f Z Wert 0 Direct Input 1 500000 0 000000 Y Refraction Index 000 1 000 Z wert 0 400000 schichtdicke RCWA diskret d Fig 3 Marking a geometry parameter for looping The mark is recognized automatically and an additional radio button together with input field s pops up after saving the change and leaving the notepad editor This 1s shown in Fig 4 If the d box is checked than the loop parameters are related to the pitch i e entering 0 2 at pitch 0 5 microns means 0 1 micron Copyright by Optimod 7 64 November 7 2014 or o 111 BSASARAYTTTANTAPARS x k i AMADA RA AAAS AR ee i 2341114000 re ooo Te s d as m T 15 LII as a Innan 1 as ERRET 7 z 93 nano ssi o ussssfisssss BILL DTI i 1 HP EEEEEIE 12 1 BHR LITA ii MENACANANADA ALLE LI i BARADAN LL 1 LII i FETTILTRITITILIILIIT a HSU eeaeae Loop Wavelength in pm Lambda jas Rayleigh Orders C Truncation E E Incidence Angle polar Theta i Start 0 End fo Step 5 ack Farameter C wildcard fo a p V TE Computation v TM Computation r Active Stack File Fig 4 Loop over a geometry parameter option occurring in the CCB Furthe
59. nput via nk file selection Here the complete path name of the file with the required index data has to specified This can either be done by typing the pathname into the corresponding field file location or by clicking the file request button marked by In the letter case a file selection box pops up and one has to make ones choice Of course the file location is not fixed However it is recommended to use the folder Unigit NKData that is generated during the installation of the UNIGIT code Basically the file extension nk is preferred to recognize refractive index data The Unigit installation comes with a couple of nk example files Feel free to complete this library according to your needs Furthermore it is possible to connect a n amp k file directly with a material ID This can be done by replacing the comment line first line of the file with the code word color followed by a colon and the material ID name see example below in Fig 46 Then when the n amp k file will be used somewhere in the stack Unigit checks the comment line when identifying a material ID compares it with the color table and when successful assigns a color to it Copyright by Optimod 52 64 November 7 2014 21 I THRRRRRRRRHH EHREHHA ANANRARURNRARNAR i TE PANA ARAN AAA Y U a ERRER ne anne me anan an nn TARA A EL e e e e ke versati le rigorous grating solver rrr LLLLI eec AS PANAMA LITILITI CLIE 1
60. o this end the polygon points have to be entered in the Polygon Points field This can be done by means of the two input fields labelled with x and z below notice that x 1s the abscissa and z the ordinate and pressing either INSERT or REPLACE Of course existing polygon points can also be deleted again While inputting the profile points one must not care about the absolute geometry Only the relative values have to be tuned to each other In addition the whole profile can be shifted laterally by specifying the phase xO In the example above a trapezium interface was defined Of course all kinds of profiles including undercuts can be defined by the suitable choice of the points and their order An example is shown below It was realized by inserting a point 0 5 0 after the third point of the previous trapezoid profile An example is shown in Fig 23 Copyright by Optimod 30 64 November 7 2014 LO URT828 12 2121 222 1252150 ih a ARANA AN ANANKAN THEHRRHEH oros grat ns s so arar H H rers T TTL RARA SHE Hh FrTTITI TIT on S TITTITIITITIT m 0730 1 000 2 Cancel ESE Replace Delete 0 lo Fig 23 Example for the input of a polygon layer 5 1 3 Rayleigh Fourier Sinus Layer The RF sinus layer resembles widely the RF polygonal layer except for the interface between the two media The layer editor window appearance is shown in Fig 24 UNIGIT Lay
61. on 0 100 Power Ange pam editor For further explanation see also the o o drawing below 0 000 0 500 0730 1000 Check the box Ortho if you want to have an ellipse in real world otherwise the ellipse is defined for the non orthogonal coordinate system 1 e it will be distorted in real world Schematically this 1s shown in the drawing below Notice the drawing does not show this however your calculation result is supposed to be different for the cases of a checked and an unchecked Ortho box Non orthogonal elementary cell Ortho Box Ortho BEox checked unchecked The checkbox 2 Ellipse enables the definition of an ellipse in an ellipse as can be seen in the figure below Copyright by Optimod 44 64 November 7 2014 Husum UNIGIT rA Editor Mame no name Layer Type Ellipse_2D Thickness f pum Refractiwe Index Medium 1 Direct Input Real Park 1 000 Imaginary Part 0 000 Refractive Index Medium 2 Ellipse Direct Input Real Part 7 500 Imaginar Part 0 000 Edit Refractive Index Medium 3 Ellipse 2 File Location D Program Filessaptimad sunigir amp NW FD ata alu nl Iw 2 Ellipse Same nk for Ellipse Resolution 256 x 256 Power bic E Cancel However the second ellipse has not necessarily to be located inside the first ellipse as the setup below shows Principally the second ellipse always overrules the first one Copyright by Optimod 45 64 November 7 2014 pa
62. or both polarizations 8x for one polarization 2 Central Control Board 2 1 Introductory Remarks The central control board is activated immediately after the UNIGIT program is started It appears as shown in Fig 2 Copyright by Optimod 5 64 November 7 2014 en Wavelength in microns Lambda jos nm I Havleigh Drders f Truncation Start E End le Step 1 Incidence Angle polar Select Theta i a5 Seen E dit NotePad Iw TE Computation e TM Computation Flexi Loop Stack File D Program Filessoaptimad surnigirsStacks salgrat 1d bt Computation Result File s f 1D Classic C 10 C Methad Show C 1D Conical c p Remove Mo File Selected Energy Error Save Result in D ste epp_v20t 02 YS2010 AResults result Shor Angles Fig 2 Central Control Board of Unigit Mainly the central control board serves for The preparation of the input files of the underlying Grating Solver Code The launch of the Grating Solver and The graphical presentation of the calculation results Besides the basic operation modes of UNIGIT can be selected just by selecting either a regular stack file extensions ust preferred though you can use other e g txt have been used with older versions of UNIGIT or a UNIGIT project file extension upr Accordingly there are two basic modes how Unigit can be operated e The regular mode e The project retrieval mode The following des
63. pyright by Optimod 12 64 November 7 2014 The display of the total computation time for the me EET the reappearance of the START button indicate the successful accomplishment of the computation run The computation time of the last run was 14 sec Start There are two particular features for the 2D solver e tcan be chosen between the Li staircase or the Lalanne mixing approach check the LA box for the Fourier transformation of the 2D grating e an accelerator for 2D crossed gratings with speed up factor up to 4 8 w o accuracy loss trade secret of Optimod can be activated by moving the slicer then the speed factor appears LU rp I POTES rim C 1D Classic C 1D C Method 1D Conical i E Save Result in IA SUL C Program Piles OPT IMOD 2 5 Result Presentation Depending on your choice in the output editor the results are either displayed in the DOS window and can be copied and pasted from there directly or they are written into file s When written into one file selection All in one it can be viewed immediately after the computation is finished in a Notepad window To this end you need just to call it by the NOTEPAD button The corresponding part of the central control board is shown below In order to retrieve other results you can utilize the request button to search for the file and then again the NOTEPAD button Save
64. r layer type 3 discrete RCWA layer type 4 and continuous RCWA 1 e gradient layer type 5 In addition to these basic layer types so called composite layers can be input polygonal RCWA layer type 6 sinusoidal RCWA layer type 7 and sequence of layers comprising an arbitrary number of layers from type 1 through type 7 in an arbitrary order As opposed to the sinusoidal or polygonal Rayleigh Fourier 3 layer the corresponding composite layers are automatically decomposed that means sliced into discrete RCWA slices of type 4 immediately before being processed A sequence of layers also called sub stack has to be stored as a file in the same way as the total stack description is stored The only difference between a complete stack and a sub stack consists in that the complete stack comprises beside the stack data the grating period as well as the superstrat and substrate description Moreover a hierarchy of sequences is not permitted 1 e a sub stack must not contain another sub stack In order to demonstrate the various options of the editor an example of a rather artificial layer stack 1s shown in the picture above In this example the stack is embedded between air with a fixed index of 1 and aluminum specified by the nk file see refraction index editor Beside the refraction indices the superstrat and the substrate are also defined by a thickness 1 e the position inside the material where the efficiencies a
65. re measured These values make sense if the phase information shall be output or if the materials are absorbing The period of the stack has to entered into the grating period x field upper left of the group field stack Being in the 2D computation mode a second input mask for the period in y direction orthogonal to x is provided automatically 4 2 Stack Editor 1C This editor enables the assembling of stack files for the C method An unlimited number of non parallel interfaces is permitted The stack editors considers the interface as a layer just like in the same way as it does for Rayleigh Fourier interfaces This arises from the layer wise Copyright by Optimod 22 64 November 7 2014 E Y CAD ji LEE z LLLITELLI IR 13 I ILL E ELLL I LLLI A BEEBE ac ag BSACARAUTVANZER RS ANANRARERERARENRENF processing Lot RCWA slices After entering one layer the ADD LAYER button i is disabled Furthermore the stack editor enables only three choices homogeneous flat layer type 1 which is not useful 1 e the simulation of flat interfaces or thin film stacks should be done with the 1D routine see 2 1 polygonal C method layer meaning interface sinusoidal C method layer meaning interface The basic dialog of this editor is shown in Fig 15 Similar icon as for the Rayleigh Fourier layers are used The layer types are uniquely identified by its names either CM Layer Polygonal or CM Layer
66. ription of the layer is stored in a file that must be selected see cursor file In addition the specified file can be edited by calling the notepad editor The composition of a file describing a RCWA soft slice 1s as follows E test ngr lox e First the number of partitions np has to be specified es is ipud e Second a refraction index specification has to be specified 1 e O for direct n amp k input 1 for reading from file 22 dispersion formula see also section 6 refraction index editor e Third the information according to the n amp k specifier has to be provided e g for 0 a n amp k value for a file name etc e Rows 2 and 3 are repeated np times An example for the data describing the gradient is shown below Copyright by Optimod 34 64 It shows 8 cc 4 with n 1 and the second half with n 2 0 5 amp k 2 5 m general it is recommended to pick a power of 2 for the number of partitions The specification of the material follows closely the Unigit standard see index refraction index editor Basically the RCWA hard and soft slice are very similar The only differences are that whereas the size of the partitions of the hard slice can be chosen arbitrarily the partitions of the soft slice are equidistant and their size is determined by the period divided by their total number Behind the scene the Fourier transform for the hard slice is done analytically whereas a FFT is applied for the soft slice 5
67. rmore in case of classical diffraction the polarization of the incident light may be chosen The selection fields are positioned at the same place where the radio button and the input fields for the azimuthal incidence angle occurs if conical diffraction computation 1s chosen The light may have TE polarization and or TM polarization In addition to these fixed one parameter loops Unigit version 2 01 02 upwards permits a flexible loop a k a batch processing Here the parameter variation 1s not limited to just one parameter Instead various combinations of certain parameters can be run The flexible mode is activated just by clicking the associated check box as depicted in Fig 5 EE NGT Cerc Coro cra NONO CL Stack Select Mew E dit NotePad Output Select Edit NotePad Project Control r Parameter to print Lambda C Truncation C Theta i Get Stack Set Input Set Stack M Flexi Loop D Program Filesaptimad sunigit S tack s testz ulf Load l Stack File D Program FilessaptimadsunigitsStacks rewas double txt Fig 5 Selecting a flexible loop batch processing W TE Computation W TM Computation In order to tell Unigit how to do the loop an Unigit Loop Control File extension ulf has to be selected An example of an ulf file 1s shown in Fig 6 The parameters have to be listed in exactly the order to be seen in the figure Furthermore the total number of parameter
68. rt 3 000 Imaginary Pare 0 000 Ar File Location CE primad sLInigiinsEall HED atasalu nk Alu Direct Input Real Part 1 500 Imaginary Pare 0 000 neU Cross Section Slice Lus _ 0 000 0250 0 _ 0 750 Irisert Replace Delete Fig 25 Layer editor for 1D RCWA slices As opposed to the homogeneous flat layer a RCWA slice is characterized by different regions or partitions with different optical properties The example shows three areas with different refraction index The first area extends from O through O and is only a sort of placeholder here It is followed by the second partition apparently Aluminum with the n amp k values stored at the shown file location which fills the area between O and 0 5 pitch The third material has the index 1 5 and fills the area between 0 5 and O pitch whereas the rest up to full pitch 1s filled by same material as the first partition here n 1 Note that it is possible in many cases to leave out the x 0 entry e g a slice with duty cycle 1 1 could look like x1 0 25 amp nl x2 0 75 amp n2 here the regions from 0 through 0 25 and from 0 75 through 1 0 pitch would be filled with nl and the remaining from 0 25 through 0 75 pitch with n2 All materials are checked for material ID s which are compared with the entrances in the color table section 3 2 If positive the according color 1s assigned and used in the cross section presentation of slice as well as 1n the stack cross section v
69. sets has Copyright by Optimod 8 64 November 7 2014 see ee ott Te IAHR ee eo ee mo versatile rigorous grating solver to be entered in the second line here 6 Beside of these constraints the parameter values in each line corresponding to a parameter set are quite arbitrary within the range of physical values Of course single loops can also be specified but as opposed to the single loop selection a variable step width can be invoked such as shown in the example of Fig 6 Finally the output parameter out of the set which shall be appear in the output file parameter to be printed can also be selected via the radio buttons compare to Fig 5 E test ulf Editor ooo q qe ak Datei Bearbeiten Format Ansicht 7 Unigit Loop File 6 Wavelength order AOI wildcard Azimuth 0 2 5 60 0 O Fig 6 Structure of an Unigit Loop File Next a stack file has to selected for the regular operation mode described here This can simply be done either by clicking the SELECT button or by clicking the NEW button which are both located in the Stack group When a stack file 1s selected the solver is automatically selected see below Moreover the stack editor see section 4 is adapted to the selected solver Eventually the solver routine has to specified This has to be done of course related to the selected stack file 1 e you can run ID RCWA based stack files only with a 1D routine 1D classica
70. ss and you can enter a name for the layer similar to other layer types Moreover you need to specify a material for the embedding medium and a file with the extension f2d which contains the bitmap description of the layer The file content 1s explained as follows 2 number of materials beside the embedding material 0 specification ID for material 1 0 direct input 1 5 0 0 n amp k for material 1 1 specification ID for material 2 1 n amp k file C Program Files OPTIMOD Unigit NKData SILICON NK pathname of the n amp k file for material 2 6 97 Fourier discretization power e g discretization 1s 2 6 amp number of lines to follow 528 0 pixel number amp material ID e g 528 pixels with material 0 embedding material 321 pixel number amp material ID e g 32 pixels with material 1 322 pixel number amp material ID e g 32 pixels with material 2 32 1 pixel number amp material ID e g 32 pixels with material 1 528 0 pixel number amp material ID e g 528 pixels with material O embedding material Note the total number of pixel description lines in this example must be 97 and the total number of added pixel numbers 1 e 528 32 32 32 528 must be equal to 2 6 2 4096 A graphical example for a non orthogonal cell is shown below First the elementary cell has to be defined as shown red color in Fig 39 Copyright by Optimod 47 64 November 7 2014 Fig 39 De
71. termination of the elementary cell As a next step one has to do the discretization in unit cell coordinates The linear pixel number has to be a power of 2 64 128 256 etc The pixel number in both axes has to be the same no matter what the pitch 1s IL y Fig 40 Filling of an arbitrary layer The counting direction is indicated by the green arrows in Fig 40 1 e scanning row by row with blanking like behaviour jump from the end of one row to the begin of the next row as shown As long as pixels have the same material defined by largest area percentage just add when material is changing save the value and restart counting across scan blanking This would result in the following f2d information for the graphical example assuming material O is white and material 1 is blue 48 0 3 lines with 16 pixel each 3 1 3 pixels blue 6 0 6 pixels white 10 1 7 pixels in row 4 right hand and 3 pixels in row 5 left hand counting across the blanking 5 0 5 pixels white etc Copyright by Optimod 48 64 November 7 2014 r7 x 7 Y i E AHANANANAR x f l MITA rrrrrerrrrrecres ay a n M o gt gt Lor eee gt delo FERRE A i B LE Ll LA LELILIT a T a a a nca RU Peele ere ee ae eee E A The installation of version 2 XX XX comes with 3 stack files that describe all the same geometry a rectangular area with n 1 5 embedded in vacuum with n 1 but with different means e stack2d_elli ust using the ell
72. tions available Copyright by Optimod 41 64 November 7 2014 9 o bh o o o v ue e o e o o o 4 a al lo LA q n 542 El Ll 0 0 dl 0 da Ll a Mana TETE E so Y versatile rigorous grating solver Flat Homogeneous Layer Thin film Patch Rectangles Layer Super Ellipse Layer Arbitrary Filling Sequence 5 3 1 Flat Homogeneous Layer The specification for homogeneous layer a k a thin film in 2D is the same as in 1D You need only to enter the thickness of the layer in microns and to specify the material by means of the refraction index editor Moreover the layer a name can be attached to the layer 5 3 2 Patch Rectangle Layer This layer type will be of advantage if your 2D area can be approximated by means of rectangular patches With the help of the editor you can specify the position of the patch as well as its material within the elementary cell In addition you need to enter the thickness of the layer An example is shown in Fig 36 UNIGIT Layer Editor X Mame patch example Layer Type Patch Thickness 0 03 pm Refractive Index Medium 1 Direct Input Real Part 1 000 Imaginar Part 0 000 Patches relative Mumber 1 1 x2 2 Refraction Index 0 1000 0 9000 0 9000 0 8000 Direct Input Real Part 1 000 Imac 0 2000 0 2000 0 6000 0 4000 Direct Input Real Part 1 800 Imac 0 000 0 000 3000 0 1000 PMMA Cauchy n1 1 478 n2 0 004 0 0000 0 3000 0 5000 0 2000 File Location E
73. y laa TL SHHHHHH LA SE LIYIITIIPII ITIN e Tr a mi ananan TT a tm ana y FA D 2 d Li HT HH H versatil O EN 4 TER py w ID rp rd n IT HE CURT LEE CANA ASA MA MORA et TS CC weep ri vi titi tieeeey TIT tir 7 T EI MOm Output Format Output Value No Output File few File Float 4 Digits f Efficiency C Allin One Append Fix 8 Digits Efficiency amp Phase Single Files 7 Sci C Amplitude amp Phase Phase Efficiency total TanPsi CosDelta v Reflection v Transmission Elficiencies in Filename R Matris TE Complex Value Diffraction Angles Filename R Matris TM T Output Orders E A Minimum 26 0 Masimum 2 o Filename T Matrix TM Iv Show Info in DOS Project File Window l Cancel Fig 49 Selecting the proj ect file generation in the output control editor 7 3 Project retrieval mode The project retrieval mode is activated when loading a project file instead of a stack file In the output editor this becomes visible by the name change from Project File compare section 7 1 to Stack File see figure below Filename T Matrix TM In case you want to retrieve the stack file from a Unigit project file see section 8 3 you have to check this box and enter a file name where to save the stack information to The extension is forced to the standard ust 1f not specified Copyright by Optimod 59 64

UNIGIT RIGOROUS GRATING SOLVER VERSION 2.01.04 USER

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