Concept of the InGaAs Plasmonic Waveguide for Quantum Cascade Laser Applications

APPLIED PHYSICS VOLUME: 19 |NUMBER: 4 |2021 |DECEMBER Concept of the InGaAs Plasmonic Waveguide for Quantum Cascade Laser Applications Adriana LOZINSKA , Mikolaj BADURA , Beata SCIANA Department of Microelectronics and Nanotechnology, Faculty of Microsystem Electronics and Photonics, Wroclaw University of Science and Technology, Janiszewskiego 11/17, 50-372 Wroclaw, Poland [email protected], [email protected], [email protected] DOI: 10.15598/aeee.v19i4.4099 Article history: Received Jan 29, 2021; Revised Jul 02, 2021; Accepted Aug 02, 2021; Published Dec 31, 2021. This is an open access article under the BY-CC license. Abstract. Quantum cascade lasers are sophisticated devices mostly based on InGaAs/AlInAs/InP heterostructures to improve thermal performance. Their structure consists of a core containing hundreds or even thousands of thin layers, covered on both sides with thick cladding waveguides. Such a laser design creates enormous stresses in the core and can cause degradation of the entire device. An alternative to the thick InP claddings are thin, highly doped InGaAs layers used as plasmonic waveguides. This solution allows to achieve a mode confinement above 50 % even at only 150 nm of the waveguide layer, which is extremely difficult in the case of standard designs. The article presents theoretical simulations concerning the influence of the InGaAs plasmonic layer on the mode confinement. Keywords InGaAs, Low-Pressure Metalorganic VapourPhase Epitaxy, plasmonic waveguide, QCL. 1. Introduction Quantum Cascade Lasers (QCLs) are unipolar devices based on intersubband transitions [1]. The design of the laser and the thickness of individual layers have a key impact on the emitted wavelength [2]. The core of QCL contains hundreds or even thousands of thin layers with a thickness of the order 0.5−10 nm. Because of the sophisticated nature of QCL, it is important to deposit layers of strictly defined composition and thickness [3]. The critical elements in QCL construction are claddings with certain free carriers concentration profiles, which ensure the distribution of the fundamental mode in the laser core. The thickness, as well as doping profile, affect not only the confinement of the mode but also the free carrier absorption (losses) and threshold gain. Usually, QCL contains core and suitably doped thick claddings e.g. based on indium phosphide. The deposition of thick layers significantly extends the time of epitaxial growth, which affects the quality of interfaces due to the long annealing process and consequently increases costs. In addition, claddings reduce heat dissipation from the core of the laser what leads to heating of the structure [4]. An alternative idea for standard thick claddings is to use thin, highly doped plasmonic InGaAs layers [5]. Thanks to this it is possible to reduce the overall thickness of the laser structure and thus decrease both duration of the epitaxy and process costs. The use of the substrate as the bottom waveguide and the thin InGaAs plasmonic layer as the top one allows the total thickness of the epilayers to be reduced by up to half. Application of InGaAs ternary alloys allows achieving a high doping concentration without decreasing a crystalline quality as well as a formation of ohmic contact, without the necessity of thermal annealing. In addition, the serial resistance of the whole device reduces, which results in lower working voltage. Epitaxial growth of InGaAs plasmonic layers is a huge technological challenge because it requires a very high doping level, exceeding 1·1019 cm−3, and both a high crystalline together with perfect optical quality. In the article, the influence of plasmonic InGaAs waveguide design on the optical losses and mode confinement, based mainly on theoretical considerations, is presented [6]. 350 ©2021 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING APPLIED PHYSICS VOLUME: 19 |NUMBER: 4 |2021 |DECEMBER 2. Results and Discussion In theoretical model, the attention was focused only on the highly doped InGaAs layer working as the top waveguide. The simulations were carried out for the wavelength of 8 µm - due to the correlation presented in the literature [5] between the doping level for InGaAs lattice-matched to InP and complex refractive index. The values of parameters, such as the refractive index n, extinction coefficient kand the corresponding doping level n0, are included in Tab. 1. Tab. 1: The values of the doping level, refractive index and extinction coefficient of InGaAs lattice-matched to InP determined for 8 µm. n0n k Doping level ·1019 cm−3 Refractive index Extinction coefficient 1.2 0.85717 0.348878 1.3 0.50000 0.628690 1.3 0.43485 0.748880 1.4 0.32769 0.976540 1.5 0.22439 1.218800 The optimal level of doping concentration and the thickness of a thin plasmonic layer were investigated in order to minimize plasmonic leakage and improve the mode confinement. The modeling approach was used for the determination of the influence of design construction on mode confinement in the laser core Γ and percentage leakage of the laser mode on the plasmonic layer Γplasmon. A dedicated python based script was written using the CAMFR full-vectorial Maxwell solver [7] as the calculating tool. Based on eigenmode expansion, structures were divided into a finite number of layers where the refractive index does not change in the z-direction. The main focus was on the electrical component of the TM mode E-TM due to selection rules for intersubband transitions in quantum wells. In the case of plasmonic layers - apart from the refractive index, an extremely important parameter is the extinction coefficient kwhich significantly affects the distribution of the laser mode [5]. Γparameter was determined from the integral of the square of the electrical component of the TM mode E2-TM in the core. In a similar way was estimated the percentage leakage on the plasmonic layer Γplasmon. The simulations were carried out for different thicknesses d(50−500 nm) and doping concentration levels n0(1.2−1.5·1019 cm−3) of the top InGaAs layer. For a better comparison of the obtained results, the value of E2-TM has been normalized. Figure 1 presents the change in the distribution of E2-TM along the whole structure as a consequence of increasing the thickness of the plasmon InGaAs top layer doped at the level of n0= 1.3·1019 cm−3. In the case of the narrow 100 nm thick InGaAs layer (a) (b) Fig. 1: Distribution of the refractive index n(black line) and the square of electrical component of the TM mode E2-TM (red line) in the QCL structure with a) 100 nm and b) 500 nm InGaAs plasmonic layer for n0= 1.3·1019 cm−3. (Fig. 1(a)), the highest intensity of the mode is observed in the plasmonic area what corresponds to significant losses in mode confinement Γand a large plasmonic leakage Γplasmon (11.2 %). Increasing the width of the InGaAs layer to 500 nm enhances the mode confinement and significantly reduces the value of Γplasmon to 3 % (Fig. 1(b)). The intensity of the laser mode is almost five times higher in the core region than in the plasmonic area which is evident in the improvement of QCL parameters. Analogous simulations were carried out for another plasmonic layer thicknesses changing from 100 −500 nm for n0= 1.3·1019 cm−3and different doping concentration levels n0varied from 1.2−1.5·1019 cm−3at d= 500 nm. Based on the obtained results the dependences of Γand Γplasmon parameters on the InGaAs top layer thickness dand carrier concentration n0were determined and shown in Fig. 2. On the basis of Fig. 2(a), it was found that with increasing thickness of the InGaAs plasmonic layer up to ©2021 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 351 APPLIED PHYSICS VOLUME: 19 |NUMBER: 4 |2021 |DECEMBER 300 nm the mode confinement increases and plasmon leakage significantly decreases, while for d > 300 nm a saturation of both dependences is observed. Such correlation for all levels of carrier concentration is observed. The impact of the carrier concentration modification at the constant thickness of the plasmonic layer d= 500 nm was also analyzed (Fig. 2(b)). As the concentration increases the mode confinement Γis slightly reduced and at the same time, the plasmonic leakage Γplasmon is significantly decreased. Waveguide losses due to leakage on the surface plasmons αplasmons can be described by the formula: αplasmons =4πnmn3 d k3 mλ,(1) where λis the wavelength, nmand kmare the real and imaginary parts of the complex refractive index of the metal (in this case they refer to nand kparameters of highly doped InGaAs layer), and ndis the real part of the complex refractive index of the dielectric material (in our case a laser core: nd= 3.36) [8]. (a) (b) Fig. 2: The dependences of Γand Γplasmon as a function of: a) top InGaAs layer thickness dfor n0= 1.3·1019 cm−3; b) top InGaAs layer doping levels n0for d= 500 nm. Fig. 3: Dependence of plasmonic losses at the interface αplasmons between the highly doped InGaAs and the core on the doping level n0. Based on Fig. 3, it was found that on a logarithmic scale the relationship between plasmonic losses at the interface and the doping level n0is linear. As the doping level increases, the losses decrease, mainly due to a strong increase in the extinction coefficient with a slightly changing refractive index. The losses on this interface are very high due to the low extinction coefficient for InGaAs compared to standard metallic layers. A very important parameter in the point of view of QCL spectral range of work is connected with absorption losses on free carriers αfc. Assuming an ideal situation when all dopant atoms are ionized giving free carriers (n0=N), the αfc value can be calculated using the Eq. (2): αfc =e2 4π2c30neff · Nλ2 m∗τ,(2) where eis elementary charge, cvelocity of light, 0vacuum permittivity, neff complex of refractive index, Ncarrier concentration, λwavelength, m∗electron effective mass and τcarrier lifetime value taken on the basis of literature τ= 150 fs [1]. Table 2 lists αfc values calculated for d= 500 nm and different doping levels n0. Losses on free carriers rise with increasing doping level, which confirms the theoretical predictions. Additionally, the parameter Γplasmon Γ, which represents the percentage of plasmon leakage relative to the mode confinement, was determined for a better comparison of the obtained results. Tab. 2: Collected parameters for a plasmonic layer with a thickness of d= 500 nm at different doping levels n0. Doping level n0(cm−3) Γ (%) Γplasmon (%) Γplasmon Γ (%) αfc (cm−1) 1.20 ·1019 53.4 3.4 6.3 3.3 1.30 ·1019 52.6 3 5.7 5.7 1.35 ·1019 52.3 2.7 5.2 5.9 1.40 ·1019 51.6 2.6 5.0 6.1 1.50 ·1019 50.9 2.3 4.5 6.4 352 ©2021 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING APPLIED PHYSICS VOLUME: 19 |NUMBER: 4 |2021 |DECEMBER (a) (b) Fig. 4: Theoretical simulations of a) standard 3 µm thick InP waveguide and b) 150 nm thick top InGaAs waveguide for n0= 1.2·1019 cm−3. Based on the data presented in Tab. 1, Tab. 2 and Fig. 3, the optimal doping level n0= 1.35 ·1019 cm−3 was estimated. For this value of n0, the mode confinement Γis still very high, above 52 %, and the plasmonic leakage Γplasmon slightly differs from the lowest value. Additionally, it is worth emphasizing that larger values of the extinction coefficient increase the absorption losses, therefore, for the discussed highest doping level, these losses could completely disturb the laser operation. In the case of the doping level of 1.35·1019 cm−3, the extinction coefficient kis slightly greater than the real part of the refractive index n(Tab. 1), which, however, gives visible effects in reducing plasmonic losses on the interface (Fig. 3). To confirm the benefits of usage of the thin InGaAs plasmonic top waveguide in QCL constructions, theoretical simulations for the standard applied thick InP waveguide were conducted. In order to ensure complete data comparison, Fig. 4 presents the standard InP waveguide and one of the simulated InGaAs waveguide design. The standard InP waveguide construction included two claddings: top and bottom consisting of two 1.5 µm steps with doping levels of 1·1017 cm−3and 3·1016 cm−3, respectively. In the case of such a design, it is very difficult to obtain a mode confinement above 50 %. In contrast for InGaAs plasmonic waveguide, most simulations indicate that this parameter is maintained at 50 % or more. It is worth emphasizing that in such a case while achieving better optical parameters the thickness of the epitaxial structure can be reduced by almost 6 µm. This significantly shortens the technological process, additionally reduces the cost, and allows to rely only on the epitaxial layers of InGaAs and AlInAs without InP. 3. Conclusions In the article, the influence of the thickness and carrier concentration level of the InGaAs plasmonic layer on the basic parameters, such as mode confinement and the percentage of leakage on the plasmons, were presented. In order to design a plasmonic layer, particular attention should be paid to the selection of parameters dand n0, because even a small change may cause the complete extinction of the radiation. On the basis of the presented results, it was found that while concentration level is constant, by increasing the width of the plasmonic layer the mode confinement increased and the leakage on the plasmons was significantly reduced. Based on the calculations it was found that a higher level of carrier concentration significantly reduces plasmonic leakage but also slightly reduces mode confinement. Calculations of plasmonic losses on the interface between the highly doped InGaAs and the laser core for different doping level n0revealed that on a logarithmic scale this relationship is linear, i.e. the higher n0concentration causes the lower plasmonic losses αplasmons. However, these losses are still very high due to the low extinction coefficient of InGaAs semiconductor layer in relation to metallic films. Comparing InGaAs plasmonic waveguides with a typical thick InP construction, it was found that even not optimized plasmonic layers give better mod confinement even with thin layers of 150 nm. Based on the presented results, the optimal doping level of 1.35 ·1019 cm−3was estimated and further scientific considerations will be conducted mainly around this level. Presented simulation results encourage further consideration and experimental confirmation. The next stage of research will be to modify the plasmonic layer constant doping profile into a stepped and gradient one to minimize plasmonic losses at the interface. ©2021 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 353 APPLIED PHYSICS VOLUME: 19 |NUMBER: 4 |2021 |DECEMBER Acknowledgment This work was co-financed by: the Polish National Centre for Research and Development grant No. TECHMATSTRATEG1/347510/15/NCBR/2018 “SENSE”, by the Polish National Science Centre under the project OPUS-17 No. 2019/33/B/ST7/02591, the Polish National Agency for Academic Exchange under the contract PPN/BIL/2018/1/00137 and Wroclaw University of Science and Technology subsidy. Author Contributions A.L. developed theoretical considerations, conducted modelling and numerical simulations. M.B. prepared the input file format for the modelling program. All the authors A.L., M.B. and B.S. the authors contributed to the final version of the manuscript. B.S. supervised the project. References [1] FAIST, J. Quantum Cascade Lasers. 1st ed. Oxford: Oxford University Press, 2013. ISBN 978-019-852824-1. [2] FAIST, J., F. CAPASSO, D. L. SIVCO, C. SIRTORI, A. L. HUTCHINSON and A. Y. CHO. Quantum Cascade Laser. Science. 1994, vol. 264, iss. 5158, pp. 553–556. ISSN 0036-8075. DOI: 10.1126/science.264.5158.553. [3] LOZINSKA, A., M. BADURA, K. BIELAK, B. SCIANA and M. TLACZALA. The influence of quantum well and barrier thicknesses on photoluminescence spectra of InGaAs/AlInAs superlattices grown by LP-MOVPE. Optica Applicata. 2020, vol. 50, no. 2, pp. 251–256. ISSN 0078-5466. DOI: 10.37190/oa200208. [4] LOZINSKA, A., M. BADURA, J. JADCZAK, K. BIELAK and B. SCIANA. Photoluminescence and Raman spectroscopies as an optical approach of stress determining in MOVPE grown quantum cascade laser structures. Optica Applicata. 2020, vol. 50, no. 2, pp. 289–299. ISSN 0078-5466. DOI: 10.37190/oa200212. [5] LU, Q.-Y., W. ZHANG, L.-J. WANG, Y. GAO, W. YIN, Q.-D. ZHANG, W.-F. LIU, F.-Q. LIU and Z.-G. WANG. Design of Low-Loss Surface-Plasmon Quantum Cascade Lasers. Japanese Journal of Applied Physics. 2009, vol. 48, iss. 12. ISSN 0021-4922. DOI: 10.1143/JJAP.48.122101. [6] SCIANA, B., M. BADURA, W. DAWIDOWSKI, K. BIELAK, D. RADZIEWICZ, D. PUCICKI, A. SZYSZKA, K. ZELAZNA and M. TLACZALA. LP-MOVPE growth and properties of high Si-doped InGaAs contact layer for quantum cascade laser applications. OptoElectronics Review. 2016, vol. 24, iss. 2, pp. 95– 102. ISSN 1230-3402. DOI: 10.1515/oere-20160013. [7] CAvity Modelling Framework. In: CAMFR [online]. Available at: http://camfr.sourceforge. net/index.html. [8] SIRTORI, C., C. GMACHL, F. CAPASSO, J. FAIST, D. L. SIVCO, A. L. HUTCHINSON and A. Y. CHO. Long-wavelength (λ≈8−11.5µm) semiconductor lasers with waveguides based on surface plasmons. Optics Letters. 1998, vol. 23, iss. 17, pp. 1366–1368. ISSN 0146-9592. DOI: 10.1364/OL.23.001366. About Authors Adriana LOZINSKA was born in 1993 in Tarnow, Poland. She received her M.Sc. from Electronics and Telecommunication in 2018. Her research interests include technology and optical characterization of InGaAs/AlInAs/InP heterostructures used in QCL. Mikolaj BADURA was born in Belchatow, Poland. He received his M.Sc. from Electronics and Telecommunication in 2012. His research interests include Metalorganic Vapour-Phase Epitaxy (MOVPE) technology of III-V semiconductors and other sophisticated optoelectronics devices. Beata SCIANA was born in Wroclaw, Poland. She received her M.Sc. from the Faculty of Electronics Wroclaw University of Science and Technology in 1990 and the Ph.D. degree in Electronics from WUST, in 2000. Her research interest include epitaxial growth (MOVPE) and material characterization of III-V semiconductor compounds for applications in advanced microelectronics and optoelectronics devices. 354 ©2021 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING