APPLIED PHYSICS LETTERS
VOLUME 77, NUMBER 24
11 DECEMBER 2000
X-ray and optical characterization of multilayer AlGaAs waveguides G. Leo, C. Caldarella, G. Masini, A. De Rossi,a) and G. Assantob) Department of Electronic Engineering and National Institute for the Physics of Matter, INFM–RM3, Terza University of Rome, Via della Vasca Navale 84, 00146 Rome, Italy
O. Durand, M. Calligaro, X. Marcadet, and V. Berger Thomson–CSF, Laboratoire Central de Recherches, Domaine de Corbeville, 91400 Orsay, France
共Received 5 July 2000; accepted for publication 13 October 2000兲 Effective-index measurements in multilayer AlGaAs waveguides are used in conjunction with x-ray reflectometry to yield refractive indices and thicknesses of the constituent layers, with the accuracy required by parametric interactions in guided-wave and photonic-band-gap structures. © 2000 American Institute of Physics. 关S0003-6951共00兲03650-0兴
The state of the art in both growth and technology of semiconductor heterostructures is nowadays able to grant ‘‘refractive-index engineering’’ great opportunities towards the realization of fully tailored integrated optics structures, in analogy with those encompassed by band-gap engineering in electronics. Remarkable results have been recently obtained in photonic crystals, novel laser schemes, and frequency generators.1 However, design constraints for resonant or phase-matched geometries are usually more strict than the standard compliance on thickness uniformity in m thick multilayers grown by molecular-beam epitaxy 共MBE兲. In addition, the required accuracies often exceed those available from known refractive indices of most semiconductor compounds, including the ternary AlGaAs dealt with here. While the resolution afforded by existing models of the AlGaAs refractive index is on the second decimal digit,2–4 they account neither for doping nor for thermal effects, both important at wavelengths approaching the band-gap boundaries, where dispersion becomes large and induced perturbations strongly affect the dielectric response. In addition, laterally oxidized AlAs layers have been recently employed for both optical confinement and form-birefringence engineering,5 adding extra flexibility to the design of the AlGaAsintegrated system: although these oxidized layers have been reported to exhibit a refractive index of 1.61 in the range 900–1600 nm,6 their optical properties strongly depend on layer thickness and oxidation conditions. Stringent requirements on the guided-wave effective index (n eff) are to be met, for instance, in realizing integrated AlGaAs/AlOx optical parametric generators, where the constraints of phase matching must comply with the use of inexpensive fixedwavelength pump sources.7 With typical temperature coefficients of about 0.3 nm/°C, the effective indices of the interacting modes need to be known with a precision of 10⫺3 . In this letter, we demonstrate how an accurate evaluation of layer thicknesses and refractive indices of AlGaAs waveguides can be achieved in a nondestructive fashion by resorting to the combined use of x-ray reflectometry and grating-assisted distributed coupling. a兲
Present address: Thomson–CSF, Laboratoire Central de Recherches, Domaine de Corbeville, 91400 Orsay, France. b兲 Electronic mail:
[email protected]
Our samples were grown by molecular-beam epitaxy on a GaAs wafer with the nominal structure Al0.75Ga0.25As 共digital alloy, 1500 nm兲/AlAs 共50 nm兲/3⫻关GaAs 共350 nm兲/ AlAs 共50 nm兲兴/GaAs 共420 nm兲, as sketched in Fig. 1. It will be shown in the following that due to a slight MBE miscalibration, the actual thicknesses of the layers are, in fact, somewhat smaller. In Fig. 1 we also show the electric-field profiles at ⫽1.31 m for TE0 and TM0 eigenmodes, as obtained by standard eigenmode calculations based on the Afromowitz model.2 In order to ascertain the actual thicknesses of the multilayer, we resorted to x-ray reflectometry.8 At a small angle of incidence, an x-ray beam is sensitive to the mean electronic density. Therefore, neglecting absorption, a thin layer is seen as a homogeneous medium with a mean refractive index n()⫽1⫺ ␦ (), with the incident wavelength and ␦ the deviation from the index of vacuum, of the order of 10⫺5 . Hence, increasing the angle of incidence, a system of ‘‘Kiessig’’ fringes appears, the period of which is related to the layer thickness.9 Thus, a remarkable accuracy of ⫾0.05 nm can be achieved for layers of about 50 nm. To infer the interface distances for a stack of thin layers, the resulting complex interference pattern can be analyzed performing the inverse fast Fourier transform 共IFFT兲 in Q space rather than
FIG. 1. Refractive-index profile of the waveguide, and tranverse-field profiles at ⫽1.31 m for TE0 共dotted line兲 and TM0 共solid line兲 modes. The multilayer structure is also sketched on the top 共GaAs, white; AlAs, black; Al0.75Ga0.25As, gray兲, with the corresponding GaAs and AlAs thicknesses A, B, and C.
0003-6951/2000/77(24)/3884/3/$17.00 3884 © 2000 American Institute of Physics Downloaded 14 Nov 2008 to 193.52.94.5. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
Leo et al.
Appl. Phys. Lett., Vol. 77, No. 24, 11 December 2000
FIG. 2. X-ray reflectivity of the waveguide. The short-period superlattice is associated with the AlAs/GaAs digital alloy. The long-period oscillations are due to the AlAs layers, while the short-period ones 共inset兲 refer to the thicker GaAs top and deep layers.
in 2 space, Q being the diffraction vector norm corrected for refraction.10 X-ray reflectometry was performed at the CuK ␣ 1 wavelength (⫽0.154 056 2 nm兲 using a high-resolution Seifert PTS goniometer equipped with a front double Ge共220兲 monochromator and a multilayer mirror to enhance the incident intensity. Back Soller slits and a knife located at 60 m from the sample surface allow us to reduce the background down to 0.05 cps. Thus, a dynamic range of 107 共in intensity兲 can be achieved in reflectivity. A typical set of experimental data is shown in Fig. 2 for the sample sketched in Fig. 1. First, we measured the thickness of the AlAs layer (B). Indeed, the repetition of this layer enhances the corresponding fringe system, and the absence of any other contributions in the 50 nm range allows the unambiguous determination of its thickness: B⫽44.3 nm. Due to the low ratio between the thicknesses of GaAs top (A) and deep (C) layers, we used IFFT to determine the distances between interfaces 共Fig. 3兲. From the aboveevaluated AlAs thickness, we could determine the extent of both GaAs top and deeper layers (A and C in Fig. 1, respectively兲 and found A⫽374.5 nm and B⫽311.7 nm, the thickness ratio A/C⬇1.201 being in substantial agreement with the nominal value. The n eff measurements were performed by distributed
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FIG. 4. Detected output signal vs incidence angle at ⫽1.31 m in a planar waveguide with a photoresist grating. TE and TM resonances exhibit different amplitudes due to unequal linear polarization components in the input field. Vertical dashed lines indicate the shifted resonances in the case of an etched grating.
input coupling of radiation to guided modes through a grating, and endfire output coupling onto a large-area Ge photodiode by standard optics. With the sample on a computercontrolled rotation stage with 0.001° resolution, the experiment consisted in scanning the angle of incidence and synchronously detecting peaks in guided light at the output. A periodic pattern was realized on the waveguide surface by a standard holographic set-up consisting of a cw He–Cd source at ⫽442 nm and a Lloyd mirror.11 After exposure and development, a submicron photoresist 共Shipley-1805兲 grating was obtained on the surface. This was either employed as such or subsequently etched in a H2SO4 solution. Wave-vector conservation in coupling a radiation 共input兲 field of wavelength to a guided mode of effective index n eff through a first-order grating of period ⌳ implies n eff⫽sin ⫹
. ⌳
共1兲
The measurement yields an angular spectrum related to the n eff of the modes. Zero-angle setting and grating period evaluation were carried out with a He–Ne source 共633 nm兲 and data were collected at several wavelengths around ⫽1.31 and ⫽1.55 m. After a Gaussian fit of the discrete resonances, we achieved precisions within 0.005– 0.01°, limited mainly by the stepper-motor repeatability. Since the sample temperature T was stabilized within 0.01 °C with thermistor/Peltier cell and feedback control, and was selected by narrow-linewidth, temperature- and current-controlled distributed-feedback sources, the error bar in n eff is associated mainly to the uncertainty on ⌳, with (/⌳ 2 )⌬⌳⫽3⫻10⫺4 . Although the influence of angle uncertainty 共weighed by cos ) would suggest grating designs for large coupling angles, we chose a period adequate for both our near-infrared wavelengths. Avoiding large angles and the associated excessive stray light, the adopted ⌳ permitted backward and forward coupling at ⫽1.55 and ⫽1.31 m, respectively. A typical angular scan at ⫽1.31 m on a planar waveguide with a 0.4- m-thick photoresist grating and ⌳ ⫽437.98⫾0.04 nm is shown in Fig. 4. Through proper control of input polarization, and by comparing the inferred n eff
FIG. 3. Inverse fast Fourier transform of the reflectivity curve in Fig. 2, performed between Q limits corresponding to 2 ⫽0.64° and 2 ⫽6.8°. The distances between interfaces corresponding to the five ticked peaks allow us to unambiguously determine the thickness of all the GaAs layers, namely, A and C. Downloaded 14 Nov 2008 to 193.52.94.5. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
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Appl. Phys. Lett., Vol. 77, No. 24, 11 December 2000 TABLE I. Refractive indices at ⫽1.31 m and ⫽1.55 m of the multilayer films, measured and calculated after Afromowitza and Adachi.b Our experiment GaAs Al0.75Ga0.25As AlAs
Ref. 2
Ref. 3
⫽1.31 m ⫽1.55 m ⫽1.31 m ⫽1.55 m ⫽1.31 m ⫽1.55 m 3.4058⫾0.0006 3.3742⫾0.0008 3.411 3.377 3.449 3.431 3.08⫾0.01 3.027⫾0.005 3.026 3.008 3.061 3.045 2.924⫾0.004 2.893⫾0.003 2.909 2.894 2.924 2.909
a
See Ref. 2. See Ref. 3.
b
values with model predictions, the six peaks are unambiguously identified as the three TE and TM lowest-order modes. This technique provides sharp and symmetric resonances 共angular widths of ⬇0.1°).12 They clearly emerge from a background associated with the undiffracted fraction of the input field that couples to substrate modes and undergoes multiple reflections. Optimization of the signal-to-noise ratio 共SNR兲 is achieved by acting on size and position of the collimated input beam relative to the grating. However, compared to the planar case 共Fig. 4兲, the SNR goes down by a factor 20 when testing rib waveguides, due to the reduced surface available for distributed coupling. Conversely, the use of a grating obtained by wet etching the sample itself improves the SNR by two orders of magnitude, with resonance angles 共and, therefore, n eff兲 consistently shifting due to additional mean perturbation onto the waveguide. An example of such shift is shown by the dashed lines in Fig. 4. It is apparent that larger ⌬ (⌬n eff) occur for higher-order modes, due to their weaker confinement. The values of n eff were inferred with an absolute precision of ⫾5⫻10⫺4 , comparable to what was reported by Kaufman et al.13 This level of accuracy is adequate for phase matching in parametric devices. By systematically varying the sample temperature from 10 to 60 °C, we also evaluated the temperature coefficients for the guided modes, with dn eff /dT⫽2.5⫻10⫺4 and 2.4⫻10⫺4 /°C at ⫽1.31 and ⫽1.55 m, respectively. From independently measured thicknesses and n eff , we derived the refractive indices of the multilayer at the above two wavelengths, through standard inversion of the eigenmode problem. These are reported in Table I, along with predictions from Afromowitz’s and Adachi’s models, respectively.2,3 The error bars associated with n共GaAs兲, n共AlAs兲, and n共AlGaAs兲 are somewhat different due to the unequal role of each layer on dispersion and n eff . In particular, 共i兲 for GaAs the results are compatible at both wavelengths with the Afromowitz values 共affected by an uncertainty of ⫾4⫻10⫺3 兲; 共ii兲 for AlGaAs the agreement with either model is less satisfactory; and 共iii兲 for AlAs the data support Afromowitz’s prediction at ⫽1.55 m and Adachi’s at ⫽1.31 m, respectively.2,3
Measured refractive indices, therefore, appear to be an essential complement to existing dispersion models, although the latter can be an important guideline with specific reference to the binary AlAs and GaAs. While the discrepancy between our experimental n eff values and model predictions could be partially explained in terms of multilayer growth conditions, it is worth stressing that the possibility to independently measure thicknesses and n eff of the same waveguide can be a crucial diagnostic tool for monitoring and optimizing MBE operation, and an excellent aid for the successful design of multilayer photonic structures. In conclusion, layer thicknesses and near-infrared effective indices of MBE-grown thick multilayer semiconductor waveguides have been carefully evaluated by combining x-ray reflectometry and grating coupling. We demonstrated that the synergy between such techniques can provide an unprecedented knowledge of the AlGaAs/GaAs/AlAs material system, with the accuracy required in the design of guided-wave structures such as integrated optical parametric oscillators. The authors are grateful to M. Morabito and L. Colace for their support in the laboratory in Rome. This work was funded by the European Union 共Project OFCORSE II兲. 1
V. Berger, in Confined Photon Systems, edited by H. Benisty, J. Ge´rard, R. Houdre´, J. Rarity, and C. Weisbuch 共Springer, Berlin, 1999兲. 2 M. A. Afromowitz, Solid State Commun. 15, 39 共1974兲. 3 S. Adachi, J. Appl. Phys. 58, R1 共1985兲. 4 E. D. Palik, Handbook of Optical Constants of Solids 共Academic, San Diego, CA, 1985兲. 5 A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjani, and J. Nagle, Appl. Phys. Lett. 68, 1320 共1996兲. 6 F. Sfigakis, P. Paddon, V. Pacradouni, M. Adamcyk, C. Nicoll, A. R. Cowan, T. Tiedje, and J. F. Young, J. Lightwave Technol. 18, 199 共2000兲. 7 G. Leo, V. Berger, C. OwYang, and J. Nagle, J. Opt. Soc. Am. B 16, 1597 共1999兲. 8 B. Vidal and P. Vincent, Appl. Opt. 23, 1794 共1984兲. 9 H. Kiessig, Ann. Phys. 共Leipzig兲 10, 769 共1931兲. 10 F. Bridou and B. Pardo, J. Phys. III 4, 1523 共1994兲. 11 X. Mai, R. Moshrefzadeh, U. J. Gibson, G. I. Stegeman, and C. T. Seaton, Appl. Opt. 24, 3155 共1985兲. 12 See, for example, P. Martin, E. M. Skouri, L. Chusseau, C. Alibert, and H. Bissessur, Appl. Phys. Lett. 67, 881 共1995兲. 13 R. G. Kaufman, G. R. Hulse, K. A. Stair, T. E. Bird, G. P. Devane, and A. L. Moretti, J. Appl. Phys. 77, 1747 共1995兲.
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