ELECTRONIC STRUCTURE OF InAs/GaAs/GaAsSb QUANTUM DOTS Josef HUMLÍČEK a,b, Petr KLENOVSKÝ a,b, Dominik MUNZAR a,b a DEPT. COND. MAT. PHYS., FACULTY OF SCIENCE, Kotlářská 2, 611 37 Brno, Czech Republic b CEITEC MU, Kotlářská 2, 611 37 Brno, Czech Republic, humlicek@physics.muni.cz Abstract The electronic structure of InAs quantum dots (QD) self assembled on GaAs and covered with the GaAs(1 y)sb(y) strain reducing layer displays several interesting features, depending on the geometry and the composition of the ternary material. The basic motivation is the possible lowering of the emission energy towards the prominent communication bands of 1.3 and 1.55 microns. Using the envelope function theory, we investigate the localization of electrons and holes. The most remarkable finding is the localization of holes outside InAs, close to the base of the dot, for larger value of the Sb content. Thus, type-ii molecularlike states are formed as the results of the strain and piezoelectric fields. The parameters of the ternary layer play a crucial role in forming the properties of the QD structures; some of them cannot be easily obtained by X-ray techniques. For this reason, we explore the possibility of efficient characterization of the very thin ternary layers in the QD heterostructures using VIS-UV reflectance spectra, and compare the results with those obtained by using X-rays. Keywords: quantum dots, GaAs, InAs, GaAsSb 1. INTRODUCTION Quantum dots (QDs) formed in semiconductor heterostructures are subject of interest due to their unique electronic and optoelectronic properties [1]. Self-assembled InAs QDs on GaAs are the best candidates for achieving the light emission in the two communication BANDGAP (ev) 1.5 1.0 0.5 GaAs 0.80 ev (1.55 µm) 0.56 0.57 0.58 0.59 0.60 0.61 LATTICE CONSTANT (nm) GaAsSb-Bandgaps 0.95 ev (1.3 µm) InAs GaSb bands of 1.3 and 1.55 µm (see Fig.1). The large lattice mismatch enables the growth of a dense population of QDs in the Stranski-Krastanow mode; the lowest exciton energy is determined by the dimensions of the dots, band offsets, and by the strain and piezoelectric fields. The properties of the dots can be tuned by using covering layers of ternary materials with larger lattice constant and lower bandgaps, such as InGaAs or GaAsSb [2]. These strain-reducing layers (SRLs) influence the growth, being responsible for substantial changes in the dimensions and densities of the QDs. Fig 1. Bandgaps and cubic lattice constants of three compound semiconductors (circles) and their alloys (solid lines). Dashed lines indicate the photon energies of the two communication bands. Here, we report on model calculations of the InAs dots on GaAs (100), covered with pseudomorphic GaAs(1 y)sb(y) SRL. Some of our results were published in [3], with the emphasis on the hole localization occurring for larger values of Sb content in the SRL. In order to compare the theoretical predictions with experimental data, the parameters of the SRL have to be obtained with a high precision. Aiming at this task, we have developed a new characterization tool based on normal-incidence reflectance in the VIS-UV range.
2. LOCALIZATION OF ELECTRONS AND HOLES We have assumed the pyramidal shape of the dot, having graded composition profile of In(x)Ga(1-x)As, with x=0.4 at the square basis of the length of 22 nm, and reaching pure InAs (x=1) at its top, 8 nm above the base [4]. The thickness of the GaAs(1 y)sb(y) SRL was 5 nm, assuming several compositions from x=0.1 to x=0.22. The dot and SRL were embedded in GaAs, with flat interfaces as shown in Fig. 2. Fig 2. Model structure of the graded InGaAs QD covered by the GaAsSb SRL. Having specified the geometry and materials, we have used the Nextnano++ system [5] to calculate the single particle states, using the 8-band envelope function scheme. The calculated wavefunctions were used to compute the probability densities for electrons and holes, with examples shown in Fig. 3. While the electrons are found to be always localized in the In-rich top of QD, the holes reside inside QD for lower values of y, and in the SRL for larger Sb concentrations (y>0.19). Contrary to previous reports [6], the holes are located close to the base of the dot, rather than above the dot. This is the consequence of the strain field, shifting the heavy-hole band edge to lower energies. We have also proposed an experiment to test this result, involving external vertical electric fields [3]. Our calculations also elucidate the role of the piezoelectric field. Namely, including only the strain field, the holes are located within a ring surrounding the square base of QD. With the piezoelectric field added, the holes move to the corners of the base along the (110) direction. Fig 3. (1-10) cross sections of the probability density (in arbitrary units) of the electrons (upper panel) and holes (middle panel) at y=0.1, and of the holes at y=0.22 (bottom panel). In the second step of our simulations, we calculated the excitonic energies using the configuration interaction method based on the single particle states [7]. The lowest transition energy is shown in Fig. 4 as a function of the Sb content of the SRL. Note the significant red shift of 84 mev when going from zero to the largest
value of y=0.22. The calculated dependence is in a very good agreement with the photoluminescence data of Ref. [2], after the latter were shifted by a small amount of 5 mev. EMISSION ENERGY (mev) 1060 1040 1020 1000 980 960 QD SRL Type I Type II QD SRL 10 12 14 16 18 20 22 Sb CONTENT (%) 1060 1040 1020 1000 980 One of the most intriguing results is the fact that the hole wavefunctions at larger Sb content resemble that of the lateral quantum dot molecules. This charge distribution is better defined, more scalable, and easier to fabricate compared to the lateral molecular arrangements. Fig 4. Calculated emission energies (full circles, right vertical scale) and experimental data of Ref. [2] (squares, left vertical scale).the crossover from type I to type II is indicated by the dashed vertical line. 3. OPTICAL CHARACTERIZATION OF STRAIN REDUCING LAYERS The ternary SRLs are typically only a few nm thick, leading to difficulties in their characterization. The optical response of the ternary material in the range of strong interband electronic transitions (VIS-UV region) depends strongly on the composition due to the shifts of prominent spectral features. Shown in Fig. 5 GaAsSb-BulkEps are the spectra of the complex dielectric function [8] 20 10 GaSb GaAs E E1 1 of both constituents of GaAsSb, indicating the substantial difference in the position of the critical points of the joint density of states, forming the spectral structure in the 4-5 ev range. The doublet DIELECTRIC FUNCTION 0-10 bulk, RT structure at lower photon energies (, ) displays the spin orbit interaction of increased magnitude when going from GaAs to GaSb. These characteristic structures shift in the alloys (mostly with noticeable bowing of the positions against composition, analogous to that of the fundamental bandgap in Fig. 1). Fig 5. Real (dashed lines) and imaginary (solid lines) parts of the dielectric functions of GaAs and GaSb at room temperature. The attenuation of an optical wave in a material can be quantified conveniently by the penetration depth, plotted for GaAs and GaSb in Fig. 6. Fairly small values (less than 10 nm) occur in the range of the strongest absorption in the range. Consequently, films thicker than about 10 nm behave as an semi-infinite material in reflectance measurements (see the spectra of both constituents in the inset of Fig. 6). On the other hand, for thinner films, the reflected signal is influenced by the reflections at the interface with the substrate and contain information on the film thickness. For the materials of Fig. 6 and their alloys, this occurs for the thicknesses of a few tens nm in the range of transitions (1.5-3.5 ev). Thus, for typical SRLs, characteristic fingerprints of the film composition and thickness can be identified in reflectance spectra measured in a broad spectral range.
The spectral structures due to the presence of the critical points of the joint density of states can be amplified by the (numerical) differentiation of measured spectra. Shown in the right panel of Fig. 7 are the second derivatives of the normal incidence reflectivities of Fig. 6, with the clearly separated spin-orbit doublets, and the well separated structures. GaAsSb-PenDepthGaAsSb GaAsSb-D2R_GaAsSb PENETRATION DEPTH (nm) 1000 100 GaAs GaSb REFLECTIVITY 0.7 0.6 0.5 0.4 0.3 GaSb GaAs d 2 R / d (ev -2 ) 5 0-5 GaSb GaAs 10 bulk, RT -10 bulk, RT Fig 6. Left panel: penetration depths and normal-incidence reflectivities (inset) calculated from the spectra of Fig. 5. Right panel: Second derivatives of reflectivities of the inset of the left panel. We have identified the useful information in normal-incidence reflectance spectra measured on a series of three uncapped pseudomorphic GaAsSb layers grown on GaAs by MOVPE [9]. The spectra shown in Fig. 7 were obtained with a fiber spectrometer (Avantes 2048) and the halogen-deuterium discharge lamps as light source. An epitaxial GaAs sample has provided the reference signal proportional to R ref, and the relative reflectance resulted from the ratio of sample/reference signals. The presence of the films is clearly seen as the deviation of the relative reflectance from unity, most pronounced in the and ranges. Further amplification of the sharp structures is seen in the numerically differentiated reflectances, shown in the right panel of Fig. 7. 1.10 R ref SRLcapping-RRefl-GaAsSb4 0.5 R ref SRLcapping-RRefl-GaAsSbDer1 R/R ref 1.05 1.00 843B d(r/r ref ) / de (ev -1 ) -0.5 0.95-1.0 2 3 4 5 2 3 4 5 Fig 7. Left panel: measured relative reflectances of three epitaxial GaAsSb films on GaAs.Right panel: numerical derivatives of the measured reflectances.
The target film thicknesses of the films were 10 nm, comparable with the minimum penetration depth of light in the range of the transitions. Thus, the reflected signal in this spectral range is approximately independent of the film thickness, being determined by the composition. For small Sb contents, the spectral shift of the transitions should produce a derivative-like pattern in the relative reflectance, with the magnitude proportional to the shift of the critical point energy (i.e., Sb content). We can estimate the latter in a very simple way; the expanded derivative spectra of Fig. 8 show a clear band centered slightly below 5 ev. The second derivative of the reflectivity of GaAs close to 5 ev reaches the minimum value of -3.0 ev -2 (Fig. 6), the minimum value of the differentiated relative reflectance is -0.35 ev -1 SRLcapping-RRefl-GaAsSbDer1dd for the sample #; using the linear dependence of the E R 2 ref 0.2 position on composition (with the shift of 0.76 ev between GaAs and GaSb), we arrive at the Sb content of y=0.15. Evidently, the smaller magnitude of the band for the two remaining samples witnesses the smaller Sb content (about 7 in sample #). d(r/r ref ) / de (ev -1 ) -0.2-0.4 4.0 4.2 4.4 4.6 4.8 5.0 5.2 Fig 8. Numerical derivatives of the measured reflectances of Fig. 7 on expanded scales, range. At lower photon energies, the penetration depth of light is larger than the film thickness and the measured spectra can be used to determine its value. We have identified the range of transitions as a suitable candidate for this purpose. In fact, Its shift from GaAs to GaSb is similar to that of the transition, which simplifies the analysis of the spectra. We 0.4 0.2 SRLcapping-RRefl-GaAsSbDer1ddd R ref have modeled the dielectric function of the ternary alloy in this spectral range by that of GaAs, rigidly shifted to lower photon energies by the amount proportional to the Sb content (as obtained from the spectral range). These optical constants were subsequently used to compute the -0.2 reflectivity of the film/substrate system, and its numerical derivative with respect to the photon energy. d(r/r ref ) / de (ev -1 ) -0.4 3.0 3.1 3.2 3.3 Fig 9. Numerical derivatives of the measured reflectances of Fig. 7 on expanded scales, range. The magnitude of the spectral structure centered at ~3.1 ev is proportional to the film thickness and allows us to determine its value from the comparison with measured data (Fig. 9). In a fair agreement with X-ray data [10], the film thickness of about 7 nm has been found for sample #. Further, the remaining films are thicker, indicating a decrease of the growth rate with increasing Sb content.
The main source of uncertainties in our characterization procedure consists in the influence of the (unknown) bowing of the bandgap-composition dependences for the and transitions of the strained layers. It would be desirable to measure the positions of the critical point energies on layers with known compositions. 4.CONCLUSIONS We have identified a spectacular behavior of the localization of holes in the QDs covered by GaAsSb SRLs with different Sb content. It is related to the pronounced redshift of the lowest optical transitions with increasing Sb concentration, and contributes substantially to the flexibility of the GaAs/InAs/GaAsSb system. We propose a simple characterization procedure for the SRLs, based on the spectral fingerprints provided by the strong interband and transitions in the normal-incidence reflectance. It provides considerable sensitivity to both composition and layer thickness, and is potentially useful as an in-situ monitoring technique during the growth of the structures. ACKNOWLEDGEMENTS We would like to thank A. Hospodková, K. Kuldová, V. Křápek, E. Hulicius, J. Oswald, and J. Pangrác of IOP CAS Prague for a fruitful cooperation. The work has been supported by the Institutional Research Program MSM 0021622410 and and the GACR grant No. GA202/09/0676. LITERATURE [1] D.Bimberg, M.Grundmann, and N.N. Ledentsov, Quantum Dot Heterostructures (Wiley, Chichester, 1999). [2] H. Liu et al., Appl. Phys. Lett. 86, 143108 (2005). [3] P. Klenovský et al., Appl. Phys. Lett. 97, 203107 (2010). [4] J.M. Ulloa et al., Appl. Phys. Lett. 90, 213105 (2007). [5] S. Birner et al., IEEE Trans. Electron Devices 54, 2137 (2007). [6] S. Rodt et al., Phys. Rev. B 71, 155325 (2005). [7] C. Y. Jin et al., Appl. Phys. Lett. 91, 021102 (2007). [8] P.Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer, Berlin 2001). [9] A. Hospodková et al., unpublished. [10] O. Caha, unpublished.