Refractive index profile measurement techniques byreflectivity profiling: vidicon imaging, beamscanning, and sample scanning
Jochen Steffen, Andreas Neyer, Edgar Voges, and Norbert Hecking
The refractive index profiles of titanium-diffused LiNbO3 planar and channel waveguides are determineddirectly by measuring the reflectivity of angular polished surfaces. Three measurement techniques aredescribed and compared: (1) large area illumination of the angular polished waveguide and imaging of thereflected light to a vidicon, (2) scanning of a focused beam across the sample, and (3) scanning of the sampleunder a focused beam. Preference is given to the last method which provides an accuracy of An/n = 10-4 witha local resolution of the index profile of <0.1 Am in depth and -1um in width.
1. Introduction
The modeling and fabrication of integrated opticalcomponents in LiNbO3 with well-defined characteris-tics require an accurate knowledge of the refractiveindex profiles of the realized waveguides. There al-ready exists a number of methods to determine theseprofiles indirectly from interference experiments onthin polished slices1 and from the inverse WKB meth-od in conjunction with the m-line spectroscopy.2 4The most severe restrictions of these indirect methodsare the small number of measurement points (typically<10) and, in the case of the inverse WKB method, thelimitation to planar waveguides (no channel wave-guides) with monotonic index profiles (no buriedwaveguides).
A direct method to determine the refractive indexprofiles of LiNbO3 by measuring the reflectivity ofangular polished waveguide surfaces has been reportedin Ref. 5. The principle of this method is based on thechange of the reflectivity AR = R- R, with RW and R3,the reflectivities of the waveguide and the substrate,directly proportional to the change in the refractiveindex An:
An/n8 = 1/4(n, - 1/ns)AR/R,. (1)
All authors are with Universitat Dortmund, Postfach 500500, D-4600 Dortmund 50, Federal Republic of Germany. N. Hecking is inLehrstuhl fur Experimentelle Physik I, and the other authors are inLehrstuhl fur Hochfrequenztechnik.
Received 1 February 1989.0003-6935/90/304468-05$02.00/0.
Here, nS is the refractive index of the substrate. Thissimplified formula is based on the Fresnel reflectioncoefficient for normal incidence and may be applied upto reflectivity changes of -10%. The contribution ofthe refractive index profile below the surface to thesurface reflectivity has been calculated6 to be of theorder of ARR 10-5 for a Gaussian index profile.This is 1 order of magnitude below the resolution of themethods described here and therefore may be neglect-ed.
To increase the local resolution of the refractiveindex profile into the depth, the waveguides are pol-ished at a very shallow angle of -1° (Fig. 1). By thisprocedure, the waveguide depth d is magnified by afactor of 1/sin a (I 60 for a = 1) yielding a resolution<0.1 ,um.
Concerns about a possible distortion of the mea-sured refractive index profiles due to the polishingprocedures could not be verified by comparison of theresults obtained here with refractive near field mea-surements (for glass waveguides) and with m-line spec-troscopy (for Ti:LiNbO 3 waveguides).
11. Experimental Methods
Three experimental techniques have been employedfor the reflectivity profile measurements: (1) imagingof the reflected light to a vidicon array camera, (2)scanning of a focused light beam across the angularpolished surface (beam scanning), and (3) scanning ofthe sample under a focused beam (sample scanning).
A. Vidicon Method
The experimental setup for measuring the indexprofiles of planar waveguides by the vidicon method isshown in Fig. 2. The angular polished surface of the
Fig. 1. Side view of angular polished waveguide for reflectivityprofiling.
array vidiconto computer
monochromaticpolarized light 1
'incident-lightmicroscope
angular polished Ti: LiNbO3surface
surface side viewilluminated area
500pum top view
Fig. 2. Schematic configuration of experimental setup for reflectiv-ity profiling by the vidicon method.
sample is illuminated by monochromatic polarizedlight at normal incidence which is accomplished byusing an incident light microscope. The illuminatedarea is restricted by apertures to a stripe of 500 X 50 Amrunning perpendicular to the edge of the polished sur-face. Since the vidicon system (OMA 2, PAR) pro-vides 500 channels, the information of the area of 1 X50 gm is attributed to one channel. This correspondsto an integration or averaging of the reflected light overa 50-gm range at constant depth. The stripe width of1-gm yields a resolution into depth of -17 nm for an 1°angle of the polished surface. The advantage of thevidicon method is that no moving parts are involvedwhich may perturb the accuracy of the results and thataveraging is relatively easy by the multichannel ana-lyzer technique. The main drawback is the high dy-namic range of 80 dB (electrically) required to resolve arefractive index profile of An/n 10-2 with an accura-cy of 10-2. Commercial systems offer this dynamicrange only for Si targets, so that an evaluation of re-fractive index profiles at important infrared wave-lengths, e.g., 1300 and 1500 nm, is difficult.
Experimental results of refractive index profiles ofTi:LiNbO3 waveguides obtained with the vidiconmethod are published in Ref. 5. The same method hasbeen applied successfully in previous works for thedetermination of refractive index profiles of glasswaveguides8 and of defect structures of ion implantedsilicon. 9
photodetector computer
laser
scanner
scan direction
top view
beam splitter
I \1 polarization filter
I microscope< objective
Ti: LiNbO3 side view
Fig. 3. Schematic configuration of experimental setup for reflectiv-ity profiling by the beam scanning method.
B. Scanning Techniques
The above mentioned disadvantages are overcomeby scanning techniques (beam scanning and samplescanning). First, the dynamic range may be reducedto -40 dB for the same resolution, since scanningallows analog high pass filtering of the detector signaland thus eliminating the dc component. This is equiv-alent to a subtraction of the substrate reflectivity.However, this procedure loses the absolute value of thereflectivity profile and consequently a normalizationby a known refractive index step is required.
Second, since only one detector is required, there areno problems with the homogeneity of detector arrays.Low noise InGaAsP photodetectors may be used forthe IR region.
Finally, scanning techniques allow the implementa-tion of lasers or superluminescent diodes. This resultsin high power levels of the reflected light and thereforereduces the problems associated with the sensitivityand signal-to-noise ratio of the system.
1. Beam Scanning MethodFigure 3 shows schematically the experimental set-
up for reflectivity profiling by the beam scanningmethod. The collimated beam of a laser light source isdeflected by a scanning mirror followed by a telecen-tric beam expansion system. Scanning range and fo-cal spot size are determined by the aperture and focallength of the microscope objective. The wavelength,at which the index profile should be measured, is cho-sen by selecting appropriate laser sources while thedesired polarization is adjusted by means of a polariza-tion optics. The main drawback of the beam scanningmethod is the limited aperture of the optical systemleading easily to intensity changes of the order of -40dB (electrically) and, consequently, to measurementerrors. To suppress unwanted interferences, highquality antireflection coatings must be used as usual inlaser scanning microscopes. This requirement, how-ever, is contradictory to the desired flexibility in se-
Fig.4. Schematic configuration of experimental setup for reflectiv-ity profiling by the sample scanning method.
lecting the wavelength for the index profile measure-ment.
2. Sample Scanning MethodThe experimental arrangement for the sample scan-
ning method is illustrated in Fig. 4. Here, except forthe beam scanner, the optics are identical to that de-scribed in the previous section. The problems con-cerning the precise mechanical movement of the sam-ple has been solved by using a macro-piezo translatorwith a range of 700 gim. This element is a combinationof a piezoelectric crystal and a mechanical construc-tion in one block (Physik Instrumente, P-287.70). Aposition sensor is also included to compensate thehysteresis of the piezo by active feedback control. Alinear movement is thus obtained, but only at low scanfrequencies of -10 Hz.
In the experiments reported here a 3-Hz scanningfrequency (linear ramp) is used. The substrate reflec-tivity level (dc component) is subtracted by a high passfilter with a 3-dB frequency of 0.1 Hz. Thus, thedetector signal can be viewed directly on an oscillo-scope to get a real time image of the measured refrac-tive index profile and to optimize the focusing. Forexact numerical evaluation, analog-to-digital conver-sion is used in connection with a microcomputer.
Refractive index profile measurements are typicallyperformed by taking the average values of 256 scans.In the case of planar waveguides the scanning directionis from the surface into the depth, that is, perpendicu-lar to the polished edge. Measurement errors due topolishing imperfections are reduced by a slow simulta-neous translation of the sample parallel to the polishededge. In the case of channel waveguides, scanning isperformed parallel to the polished edge and thereforeperpendicular to the channel at constant depth.These measurements are repeated at different depthpositions yielding 2-D index profiles.
Ill. Sample Preparation
It is essential, when using the reflectivity profilingmethod, that the polished surface to be evaluated has agood optical quality, that is, good flatness (low round-ing effects at the edge) and low roughness. For Ti-
CL < // " Ti-doped region
Fig. 5. Schematic drawing of sample holder for angular polishing.
. . .
0 e no 0 e;
.5 .6 2 .X
.2 A
.1 . . . . . .m
0 1 2 3 4 5 6 7 8B 9 10
depth in prm
Fig. 6. Measured refractive index profiles of a planar x-cutTi:LiNbO 3 waveguide at X = 633 nm. Fabrication parameters areTi-thickness r = 120 nm, diffusion time t = 12 h, diffusion tempera-
ture T = 1050C.
:LiNbO3 samples, best results have been obtained bypolishing with diamond spray (particle size 0.25 gim)on lead-tin plates, which have been turned off to get adefined groove structure. The 20- X 16- X 1-mm sizesamples are glued into a specially prepared holdermade out of epoxy resin with a 6-mm wide groovemilled into it at the desired angle a of -1' (Fig. 5).The resulting surface roughness is -100 nm.
IV. Experimental Results
Typical results of refractive index measurements arepresented to demonstrate the capability of refractiveindex profiling by the sample scanning method.These measurements are correlated with titanium con-centration measurements to give the desired relation-ship between titanium concentration and refractiveindex change.
Figure 6 shows the measured ordinary and extraor-dinary index profiles of a Ti:LiNbO3 planar waveguideat the wavelength X = 633 nm. The substrate materialis congruent optical quality x-cut LiNbO3. The wave-guide has been fabricated by the in diffusion of 120 nmof titanium, thus starting with a titanium square den-sity of a = 4.55 X 1017 cm-2. This number takes intoaccount the atomic density of pure titanium (5.66 X1022 cm- 3) and a correction factor of 0.67 (see Ref. 10)for the lower density of the electron beam evaporatedlayer. The diffusion conditions are: 10500C for 12hours in a dry atmosphere of synthetic air by using the
Fig. 9. Refractive index changes as a function of the Ti-concentra-tion, from measured data.
0.
0.1.
0 2 4 6 8depth in pm
Fig. 8. Calculated refractive index profilesparameter of Fig. 6.
with the fabrication
closed platinum crucible technique" to avoid out dif-fusion.
The curves shown in Fig. 6 are the mean values of 256scans. The residual noise of the order of An/n = 2 X10-4 allows the determination of the refractive indexprofiles with an accuracy of 2 X 10-4 for the extraordi-nary and 4 X 10-4 for the ordinary index profile. Themaximum refractive index changes at the surface areAne/ne = 1.09% (An, = 2.4 X 10-2) and An0/n0 =.0.46%(An, = 1.05 X 10-2). Both profiles intersect at a depthof -6 gim due to the nonlinear relationship betweentitanium concentration and refractive index change atlowtitanium concentrations.1 To clarify this relation-ship, the titanium concentration profile of the wave-guide has been measured by an electron microprobeanalysis on the beveled surface of the sample. Theresult is shown in Fig. 7. It can accurately be approxi-mated by a Gaussian curve (solid line) of the form cTi =1.15 X 1021 cm- 3 exp(-t/4.47 gm)2 . Practically, thesame distribution is obtained analytically from diffu-sion theory,' 0 if the Arrhenius coefficients Eo, = 2.22eV and Do. = 1.165 X 108 gM2/h are used which arenearly identical with the results of Holmes andSmyth12 for x-cut LiNbO3 .
From the measured titanium concentration profilewe calculated the corresponding refractive index pro-files Ane/ne and An0/n by using the calibration curvesof Fouchet et al.'0 at X = 633 nm. The resultingprofiles in Fig. 8 show an excellent agrement with the
0width in pm
Fig. 10. Measured 2-D refractive index profile of Ti:LiNbO 3 stripewaveguide (original Ti stripe width: 5.4 jim).
measured curves, especially at higher index changes.At lower titanium concentrations there are slight dif-ferences between experimental and analytical curves,which are indicated by the different depths, at whichthe ordinary and extraordinary profiles intersect (6 gimand 7.5 gm, respectively).
The relations between the measured refractive in-dex changes (Fig. 6) and the titanium concentration(Fig. 7) are shown in Fig. 9.
The measurement of the refractive index profiles ofchannel waveguides has been performed by scanningthe angular polished surface not into the depth direc-tion (as for planar waveguides) but perpendicular tothe channels. These scans are repeated at differentdepth positions. A complete 2-D index profile isshown in Fig. 10 for X = 830 nm. The fabricationparameters are Ti layer thickness r = 85 nm, diffusiontemperature T = 10500C, diffusion time t = 10 h. Theoriginal Ti stripe width if 5.4 gim. Here, the lateralresolution of -1.5,gin is limited by the focal spot size ofthe used laser (<1 gm for X = 633 nm). In the case ofplanar waveguides, the local resolution into depth of
Fig. 11. Refractive index profiles of MgO-buried Ti:LiNbO3 wave-guide; A: original Ti:LiNbO3 waveguide, B: 100 A MgO, C: 200 A
MgO, in diffused at 950'C for 2.5 h.
<0.1 /um is given by the focal spot size divided by themagnification factor /sin az which results from theangular polishing.
While the inverse WKB method in conjunction withm-line spectroscopy can only handle index profileswhich are monotonic, the presented direct method isespecially suited for buried waveguides. Figure 11gives an example of the index profiles of Ti:LiNbO3waveguides which are treated in a second step by the indiffusion of magnesium oxide at 950'C for 2.5 hours.13These measurements are also performed at X = 830nm.
V. Conclusion
It has been shown that reflectivity profiling is wellsuited for analyzing the refractive index profiles oftitanium diffused LiNbO3 waveguides. Three differ-ent experimental methods have been tested: the vid-icon imaging, the beam scanning, and the sample scan-ning. The sample scanning technique proved to be themost simple with the best results. Preliminary mea-surements on x-cut Ti:LiNbO3 waveguides consolidatethe data basis for numerical simulations and morereliable fabrication parameters. The measuredGaussian titanium concentration profile is predictedvery well by the diffusion theory, when the Arrheniuscoefficients Eox, = 2.22 eV and Do., = 1.165 X 108 AM2/hare assumed. Further samples will be prepared tostudy in more detail the calibration curves which relatethe titanium concentration with the refractive indexchanges, specially at low titanium concentrations.
This work has shown that the reflectivity profilingmethod is applicable not only to planar waveguides,but also to channel and buried waveguides. Certainly
it may be extended to other waveguide materials ofwhich semiconductors are actually of greatest interest.
The financial support of the present work by theDeutsche Forschungsgemeinschaft and the electronmicroprobe measurements of the titanium concentra-tions by the Schott Glaswerke GmbH, Mainz, aregratefully acknowledged.
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