broadband light in the infrared, based on InAs QDs embedded into a metamorphic ..... Monolithically Grown on a Si Substrate,â ACS Photonics, 1, pp. 638â642 ...
MODELLING OF BROADBAND LIGHT SOURCES BASED ON INAS / INxGA1-xAS METAMORPHIC QUANTUM DOTS L. Seravalli*, M. Gioannini †, F. Cappelluti †, F. Sacconi §, G. Trevisi*, P. Frigeri* * CNR-IMEM, Parco delle Scienze 37a, I-43100, Parma, Italy, †Politecnico di Torino, DET - C.so Duca degli Abruzzi 24, I-10129 TORINO, Italy § Tiberlab Srl, Via del Politecnico, 1 - 00133 - Roma, Italy Keywords: Semiconductors, Quantum Dots, Metamorphic Nanostructures , Superluminescent Diodes
Abstract We propose a design for a semiconductor structure emitting broadband light in the infrared, based on InAs QDs embedded into a metamorphic 4-step-graded InxGa1-xAs buffer with x = 0.10, 0.20, 0.30, 0.40. We developed a model to calculate metamorphic QD energy levels based on realistic QD parameters and on strain-dependent material properties: results of simulations were validated against experimental values. By simulating the broadband metamorphic structure, we demonstrated that its light emission can cover the whole 1.0 - 1.7 µm range with a bandwidth of 550 nm at 10K. The emission spectrum was then assessed under realistic electrical injection conditions, at room temperature, through device-level simulations based on a coupled drift-diffusion and QD dynamics model. As metamorphic QD devices have been already fabricated with satisfying performances we believe that the present proposal is a viable option to realize broader band lightemitting devices such as superluminescent diodes.
1 Introduction In the past ten years there has been an increasing interest in the development of broadband light sources in the infrared range based on quantum dots (QDs) and broadband superluminescent diodes (SLD) based on QDs have already been fabricated for medical applications such Optical Coherence Tomography (OCT) [1-3]. To achieve broad spectral bandwidth, the use of InAs/GaAs QDs QDs with modified energy levels has been proposed, resulting in an emission the 1.3 µm range at RT with a bandwidth up to 170 nm. [4] The growth of InAs QDs on InGaAs metamorphic buffers (MB) has been demonstrated as a successful approach to tune the emission of InAs QDs in the telecom window [5,6]; moreover, metamorphic QD devices have been fabricated with satisfying performances in terms of emission efficiencies. [7,8] In these last years, we have demonstrated how the metamorphic approach is a flexible design that provides more degrees of freedom to control properties of interest for QD nanostructures grown on GaAs substrates [9,10]. Here we propose an original structure design based on the growth of step-graded InGaAs buffers with embedded InAs QDs, aiming to achieve a larger bandwidth of emission at
room temperature in the relevant range of 1.0 - 1.7 µm range. This proposal relies on model calculations of confined ground levels for InAs QDs grown on InGaAs metamorphic layers, based on realistic metamorphic QD input parameters and carried on with the TiberCAD software. [11,12] In particular, values of strain of different layers of the stepgraded InGaAs buffers are calculated on the basis of best models presented in literature, in order to have reliable input parameters for InAs/InGaAs mismatch values to be fed in the model. Moreover, the model predicted values are validated against experimental data, assuring confidence in the present calculation. Then, on the basis of the calculated energy levels, we derived the expected emission spectra of structures based on InAs QDs embedded in each layer of a 4-step InxGa1-xAs MB with x = 0, 0.10, 0.20, 0.30, 0.40. The proposed multilayer structure was then inserted into a realistic p-i-n device to analyse its capability to produce a broadband emission spectra under electrical pumping and room temperature conditions. The device was simulated by exploiting an in-house software able to cope with the transport of carriers in the barrier and the carrier dynamics in the QD [13,14]. In this way, we were able to verify that under electrical pumping the design can assure an almost uniform carrier filling of the QDs in the different metamorphic layers.
2 Structure design and model details In Figure.1 we show the design of the proposed structure: a 4step graded InGaAs metamorphic buffer (MB), in which InAs QDs are embedded in each InxGa1-xAs layer, including a first layer of QDs embedded in GaAs. The thickness of each layer is 100 nm and QDs are inserted in the middle.
Figure 1: Schematic of the structure
We calculated the values of strain for the InGaAs on the basis of the model by Romanato et al. [15], without taking in consideration the QDs. Values of strain ε and of composition x are shown in Figure 2 as functions of the thickness. From this calculation, we derived the exact values of the lattice parameter aMB(x) for each step of the MB and, than, exact values of x and aMB(x) for each step of the InGaAs MB were used as input parameters for the calculation of confined ground levels of InAs QDs inserted in each grading step.
Figure 2: Dependence of composition (green) and strain (blue) on thickness We used the multiscale simulation software TiberCAD, where the strain and deformation fields are found by minimizing the elastic energy of the system and quantum mechanical models based on the envelope function approximation (EFA) are used for the calculation of eigenstates of confined particles in nanostructures. In this work, a single InAs QD with truncated conical shape and base diameters and heights taken from experimental data was considered [5,9], and the presence of an InAs wetting layer (WL) was also taken in consideration, using parameters that depend on the MB properties. [16] Strain calculations have been performed, assuming as a substrate material the InGaAs MB layer, strain tensor components of each QD, induced by the mismatch between the QD and the InGaAs MB, were obtained and fed in the TiberCAD quantum model. The calculated deformation potentials were applied to InAs bands and the Schroedinger equation was solved by using a single-band, effective-mass approach for electrons and a 6 bands k•p approach for holes. The value of band discontinuities between InAs and InGaAs MBs was taken at 0.80 [17,18], as it was recently shown that this value stands also for GaAs/InGaAs heterostructures with strained InGaAs [19], while a modified value of the QD electron effective mass is necessary to consider the strained material: we followed advice of Ref. 18 taking a value of 0.022 m0. To have a confident validation of the model we checked the predicted values of QD energy levels against experimental data available for metamorphic QDs, also for structures with InAlAs barriers. In Figure 3 we compare 10 K PL emission wavelengths from metamorphic QDs [5,20] and energy difference between electron and heavy hole ground levels as calculated from the model, considering 20 meV due to excitonic effects. From Figure 3 it can be appreciated the good agreement between model and experimental values, with discrepancies
never higher than 20 meV, that can accounted for by the experimental uncertainties in AFM measurement of QD dimensions and in experimental calibration of x.
Figure 3: Experimental (open symbols) and model calculation (filled symbols) of 10 K PL emission of metamorphic QDs as functions of the QD-MB mismatch for x = 0.15 (circles), x = 0.28 (squares) and x = 0.31 (diamonds). Dashed arrows indicate the effect of InAlAs barriers on emission energies. Dotted lines are guide for the eye. 2.1 Simulation of 10 K spectrum We derived the expected PL emission spectra at 10 K of the structure shown in Figure 4, by taking the calculated QD emission energy for each of the 5 InxGa1-xAs layers. We considered a Gaussian emission band (related to QD ensembles dishomogeneities) centered at the calculated emission energies and with the fwhm usually found in these type of structures: 50 meV for x = 0, 60 meV for x = 0.10 and 0.20, 90 meV for x = 0.30 and 100 meV for x = 0.40. [5]
Figure 4: Expected emission spectrum at 10 K of the metamorphic broadband light source (dashed lines) as function of wavelength: the spectra of each layer of metamorphic QDs are also shown.
The very broad spectrum shown in Figure 4, centered at around 1.4 µm and covering a window of about 550 nm, shows how it is possible to extend the metamorphic QD emission to long wavelengths and, hence, to obtain a very broad emission. In real structures emission efficiencies are going to be different for each layer due to extrinsic parameters such as QD density, presence of structural defects, kinetic processes. However, such effects have already been studied in these type of structures and methods to compensate for differences in the emission intensity are available. [7,21]
3 Device simulation To consider the suitability of the proposed design for a device operating at RT, we simulated the electroluminescense (EL) spectrum by exploiting a physics-based model coupling driftdiffusion equations for bulk carriers and phenomenological rate equations for QDs [14,22]. We considered a p-i-n structure with GaAs on the bottom pside and with In0.3Al0.29Ga0.41As on the top n-side, lattice matched to the MB and with an energy gap equal to GaAs. The thermal equilibrium energy band diagram of the p-i-n structure is shown in Fig. 5.
It is worth noticing that the simulation accounts for the different energy levels of the QD confined states (see Fig. 3) in each metamorphic layer that in turn affect the escape time constants [23] under the assumption that thermal escape is the sole process for carrier extraction out of the QD states. Thus, in an ideal experiment wherein the bulk states are evenly populated, the ground state (GS) of each dot layer would have different occupation probabilities due to the different position of the GS respect to the corresponding barrier energy. Under this hypothesis, the layers with larger x would have less filled GS, because being less confined this GS is closer to the barrier state and thermal escape would be favoured. Under this condition a wide and flat spontaneous emission spectrum would be impossible because of the non-uniform filling of the layers. However, as shown in Fig. 6, under realistic electrical injection conditions, transport through the ladder-like bands favours QD filling in the lower gap metamorphic layers thus allowing for the broadband EL spectrum at RT reported in Fig. 7. These preliminary simulations suggest that promising performance could be obtained by further engineering the metamorphic epilayer structure with the aim at realizing a symmetric graded index structure allowing for electrical and optical confinement.
Figure 5: Thermal equilibrium energy band diagram of the simulated p-i-n device embedding the metamorphic layers within the intrinsic region.
Figure 7: Simulation under forward bias condition (V=0.9 V): (a) Occupation probability of electrons and holes in the GS; (b) Electroluminescense spectrum. The corresponding current density is 100 A/cm2.
4 Conclusions
Figure 6: Energy band diagram of the p-i-n device under forward bias (V=0.9 V); EFn,p indicate the quasi-Fermi levels for the barrier states and EFn,pQD the quasi-Fermi levels for the electron and hole GS.
We conclude that, by inserting InAs QDs into InGaAs layers of a step-graded metamorphic InGaAs buffer, it should be possible to obtain a semiconductor structure emitting light in the infrared range (1.0 - 1.7 µm) with a broad spectrum. By using the TiberCAD 2.0 software we carried on model calculations of the QD levels considering realistic material parameters, taking in account the effect of strain on all
relevant parameters (QD-MB lattice mismatch, band gaps, electron effective masses, band offsets) and validating the model with experimental emission energies. We simulated a structure composed by a 4-step graded InGaAs metamorphic buffer with QDs embedded in each layer (x = 0, 0.1, 0.2, 0.3, 0.4), to derive the expected emission spectrum that covers the whole 1.0 - 1.8 µm range with a 550 nm bandwidth at 10K. We then simulated the electroluminescense spectrum of a realistic device at RT operation, wherein the metamorphic layers are embedded into the intrinsic region of a p-i-n structure. Hence, we foresee that a broadband device based on metamorphic InAs/InAlAs/InGaAs QDs could be developed and good performances could be expected.
Acknowledgements The work has been partially supported by the “SANDiE” Network of Excellence of EC, contract no NMP4-CT-2004500101 and by COST Action "Nanoscale Quantum Optics". Authors thank Dr Matthias Auf der Maur for useful discussions.
References [1] N. Ozaki, K. Takeuchi, S. Ohkouchi, N. Ikeda, Y. Sugimoto, H. Oda, K. Asakawa, and R. A. Hogg, “Monolithically grown multi-color InAs quantum dots as a spectral-shape-controllable near-infrared broadband light source,” Appl. Phys. Lett., 103, p. 051121, (2013). [2] S. M. Chen, K. J. Zhou, Z. Y. Zhang, D. T. D. Childs, M. Hugues, A. J. Ramsay, and R. A. Hogg, “Ultra-broad spontaneous emission and modal gain spectrum from a hybrid quantum well/quantum dot laser structure,” Appl. Phys. Lett., 100, p. 041118, (2012). [3] S. Chen, M. Tang, Q. Jiang, J. Wu, et al. “InAs/GaAs Quantum-Dot Superluminescent Light-Emitting Diode Monolithically Grown on a Si Substrate,” ACS Photonics, 1, pp. 638–642, (2014). [4] N. Ozaki, T. Yasuda, S. Ohkouchi, E. Watanabe, N. Ikeda, Y. Sugimoto, and R. A. Hogg, “Near-infrared superluminescent diode using stacked self-assembled InAs quantum dots with controlled emission wavelengths,” Jpn. J. Appl. Phys., 53, p. 04EG10, (2014). [5] L. Seravalli, M. Minelli, P. Frigeri, S. Franchi, G. Guizzetti, M. Patrini, T. Ciabattoni, and M. Geddo, “Quantum dot strain engineering of InAs⁄InGaAs nanostructures,” J. Appl. Phys., 101, p. 024313, (2007). [6] L. Seravalli, G. Trevisi, P. Frigeri, D. Rivas, G. MunozMatutano, I. Suarez, B. Alen, J. Canet, and J. P. MartinezPastor, “Single quantum dot emission at telecom wavelengths from metamorphic InAs/InGaAs nanostructures grown on GaAs substrates,” Appl. Phys. Lett., 98, p. 173112, (2011). [7] Z. Mi, P. Bhattacharya, and J. Yang, “Growth and characteristics of ultralow threshold 1.45 µm metamorphic InAs tunnel injection QD lasers on GaAs,” Appl. Phys. Lett., 89, p. 153109, (2006). [8] J.A. Czaban, D.A. Thompson, “Semiconductor optical amplifiers grown on metamorphic substrate for long wavelength application”Nanotechnology,21,p.134005,(2010).
[9] L. Seravalli, P. Frigeri, L. Nasi, G. Trevisi, and C. Bocchi, “Metamorphic quantum dots: Quite different nanostructures,” J. Appl. Phys., 108, p. 064324, (2010). [10] L. Seravalli, G. Trevisi, and P. Frigeri, “Design and growth of metamorphic InAs/InGaAs quantum dots for single photon emission in the telecom window,” CrystEngComm, 14, pp. 6833–6838, (2012). [11] TiberCad simulation package. http://www.tibercad.org. [12] F. Sacconi, M. Auf der Maur, A. Di Carlo, “Optoelectronic Properties of Nanocolumn InGaN/GaN LEDs,” IEEE Transactions on Electron Devices, 59, pp. 2979–2987, (2012). [13] F. Bertazzi, F. Cappelluti, S. D. Guerrieri, F. Bonani, G. Ghione, “Self-consistent coupled carrier transport full-wave EM analysis of semiconductor traveling-wave devices,” IEEE Trans. Microwave Theory Techn., 54, pp. 1611–1618, (2006). [14] M. Gioannini, A. P. Cedola, N. Di Santo, F. Bertazzi, and F. Cappelluti, “Simulation of quantum dot solar cells including carrier intersubband dynamics and transport,” IEEE J. Photovoltaics, 3, pp. 1271–1278, (2013). [15] F. Romanato, E. Napolitani, A. Carnera, A. Drigo, L. Lazzarini, G. Salviati, C. Ferrari, A. Bosacchi, and S. Franchi, “Strain relaxation in graded composition InxGa1-xAs/GaAs buffer layers,” J. Appl. Phys., 86, pp. 4748–4755, (1999). [16] L. Seravalli, G. Trevisi, and P. Frigeri, “Calculation of metamorphic two-dimensional quantum energy system: Application to WL states in InAs/InGaAs metamorphic quantum dots,” J. Appl. Phys., 114, p. 184309, (2013). [17] L. Wang, J. Kim, and A. Zunger, “Electronic structures of [110]-faceted self-assembled pyramidal InAs/GaAs quantum dots,” Phys. Rev. B, 59, pp. 5678–5687, (1999). [18] O. Stier, M. Grundmann, And D. Bimberg, “Electronic and optical properties of strained quantum dots modeled by 8-band k center dot p theory,” Phys. Rev. B, 59, pp. 5688–5701, 1999. [19] M. Yahyaoui, K. Sellami, K. Boujdaria, M. Chamarro, and C. Testelin, “Band parameters of InGaAs/GaAs quantum dots: electronic properties study,” Nanotechnology, 28, p. 125018, (2013). [20] L. Seravalli, G. Trevisi, P. Frigeri, S. Franchi, M. Geddo, and G. Guizzetti, “The role of wetting layer states on the emission efficiency of InAs/InGaAs metamorphic quantum dot nanostructures,” Nanotechnology, 20, p. 275703, (2009). [21] N. N. Ledentsov, V. A. Shchukin, T. Kettler, K. Posilovic, D. Bimberg, et al. “MBE-grown metamorphic lasers for applications at telecom wavelengths,” J. Cryst. Growth, 301, pp. 914–922, (2007). [22] A. P. Cedola, M. Gioannini, and F. Cappelluti, “Impact of carrier dynamics on the photovoltaic performance of quantum dot solar cells,” IET Optoelectronics, 9, no. 2, pp. 69–74, (2015).
