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The effect of temperature on the linear polarization of the photoluminescence of an ordered AlGaInP semiconductor alloy
Journal of Luminescence 195 (2018) 334–338
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
The effect of temperature on the linear polarization of the photoluminescence of an ordered AlGaInP semiconductor alloy
T
⁎
T. Prutskija, , P. Seredinb, G. Attolinic a
Instituto de Ciencias, BUAP, Privada 17 Norte No. 3417, Col. San Miguel Hueyotlipan, 72050 Puebla, Pue., Mexico Voronezh State University, Universitetskaya pl., 1, 394006 Voronezh, Russia c IMEM/CNR, Parco Area delle Scienze 37/A, 43010 Parma, Italy b
A B S T R A C T The photoluminescence (PL) emission of atomically ordered III-V epitaxial alloys grown by MOVPE is frequently polarized. We analyze the linear polarization of the PL emission from the (001) surface of an epitaxial semiconductor quaternary AlGaInP alloy with high atomic ordering parameter. We measured and calculated the temperature dependence of the PL polarization for a wide temperature range (10–300 K). Comparing the measured polarization patterns with patterns calculated using constant values of the atomic ordering and elastic biaxial strain parameters, we found that the calculations do not predict correctly the PL polarization patterns at low temperature. Furthermore, our measurements show that at room temperature the measured and calculated PL polarization degrees are almost the same, while at low temperature the measured values are smaller than those predicted by the model used for the calculations. We discuss the factors that could cause this discrepancy and conclude that it can be attributed to the complex internal structure of the layer.
1. Introduction The quaternary (AlxGa1−x)0.5In0.5P alloy is an important III-V material almost lattice matched to GaAs for any value of x and suitable for fabrication of optoelectronic devices working in the red, orange, and yellow wavelength range [1,2] For values of x greater than 0.52 the alloy becomes an indirect-gap semiconductor, and thus, the (AlxGa1−x)0.5In0.5P alloy with x =0.52 is the III-V alloy with the largest direct bandgap and lattice-matched to GaAs substrates. It is well known that in ternary and quaternary III-V alloys grown by metal-organic vapor phase epitaxy (MOVPE) atomically ordered clusters are spontaneously formed during the growth process [3,4]. Atomically ordered IIIV ternary alloys have a superstructure in which monolayers rich in one of the group III (or group V) elements alternate with monolayers rich in the other element of the same group present in the alloy. In the GaInP alloy, for example, the atomically ordered structure consists of a superlattice structure made of alternate In-rich and Ga-rich {111} diagonal planes, with interleaving planes of P atoms, corresponding to the CuPt type of ordering. Since the difference between the covalent radius of the Al and Ga atoms is small, the structural, elastic, and electronic characteristics of the AlInP and GaInP alloys are similar. It has been shown that atomic ordering of the same CuPt type also occurs in (AlxGa1−x)0.5In0.5P quaternary alloys grown by MOVPE [5,6]
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coexisting with biaxial strain due to the difference between the lattice constants of the epitaxial layer and the substrate. Atomic ordering changes the cubic symmetry of the disordered III-V alloy and splits the valence band maximum, separating the heavy-hole (HH) and light-hole (LH) valence bands at the center of the Brillouin zone [4,7]; as a result of this crystal symmetry transformation, the PL emission of the alloy becomes polarized. Additionally, the mismatch between the substrate and epitaxial-layer lattice constants causes a deformation of the layer crystal lattice, and leads to the presence of elastic biaxial strain in the layer. Strain also changes the crystal symmetry and influences the polarization of the PL emission. In previous works, we have made approximate calculations to find the polarization of the PL emitted by ordered III-V alloys [8,9]. In these calculations, parabolic bands and vertical transition rates equal to k = 0 transition rates were assumed to calculate, the polarization of the PL emission propagating along any crystallographic axis for different values of the parameters of ordering and biaxial strain. We used the same approximations in this work to calculate also the effect of temperature on the PL polarization. Here, we analyze the temperature dependence of the polarization of the PL emission of a highly ordered epitaxial layer of Al0.14Ga0.37In0.49P alloy grown by MOVPE on a (001)-oriented GaAs substrate. We measured and calculated the degree of polarization of the PL emission from
Correspondence to: Departamento de Fisicoquimica de Materiales, Instituto de Ciencias, Privada 17 Norte, No 3417, Col. San Miguel Huyeotlipan, 72050 Puebla, Pue., Mexico. E-mail addresses: [email protected] (T. Prutskij), [email protected] (P. Seredin).
https://doi.org/10.1016/j.jlumin.2017.11.016 Received 28 June 2017; Received in revised form 9 November 2017; Accepted 13 November 2017 Available online 21 November 2017 0022-2313/ © 2017 Elsevier B.V. All rights reserved.
Journal of Luminescence 195 (2018) 334–338
T. Prutskij et al.
the (001) surface of this layer at different temperatures, and we analyzed the temperature behavior of the PL emission. In contrast with the calculations, the experimentally found PL polarization degree has a non-monotonic temperature dependence. We discuss here the reasons that could lead to this discrepancy. To the best of our knowledge, this is the first study of the temperature dependence of the polarization of the PL emission from the (001) surface of a III-V semiconductor alloy with high atomic ordering. 2. Material and methods The Al0.14Ga0.37In0.49P epitaxial layer was grown on a (001) GaAs substrate at 725 °C by the MOVPE technique in a horizontal reactor with a rotating wafer susceptor. A 300-nm-thick GaAs buffer layer was grown before the Al0.14Ga0.37In0.49P layer deposition. Trimethylaluminium, trimethylgallium, and trimethylindium were used as group-III sources, and phosphine as group-V precursor. The molar ratio V/III in the gas phase was of 80, the growth rate was of 5 Å/s, and the layer thickness was approximately of 0.5 µm. After the growth of the layer was complete, the layer surface morphology was examined by scanning electron microscopy, the layer atomic content was measured by Energy-Dispersive X-ray Spectroscopy (EDS), and the mismatch between the layer and substrate lattices was determined from rocking curves measured by high-resolution X-ray diffraction (HRXRD). The temperature dependence of the linear polarization of the PL emission was measured within the temperature range from 10 to 300 K. A conventional experimental set-up, including a close-cycle He cryostat, a TRIAX550 monochromator, and a liquid-nitrogen-cooled chargecoupled-device detector, was used for measuring the PL emission from the surface of the layer. Optical excitation for PL was provided by a solid state laser with a wavelength of 532 nm. To measure the PL polarization, a quartz depolarizer and a rotating linear polarizer were mounted before the sample surface. Thus, the exciting laser beam was depolarized and then linearly polarized before focusing on the sample surface, and the PL emission was collected by the same objective, after having passed through the same polarizer and depolarizer as the incident beam. Therefore, we detected the light polarized along the same direction as the exciting beam. To avoid the polarization due to the monochromator grating, another depolarizer was installed at the entrance slit of the monochromator. The diameter of the laser spot on the sample surface was of about 2 mm, and the lowest possible excitation intensity, of approximately 1–3 mW, over all the area, was used. To obtain the integrated intensity of the PL emission from the surface of the layer, the area under the corresponding PL peak was calculated by integration of the PL curve. In what follows, Al0.14Ga0.37In0.49P will be abbreviated as AlGaInP.
Fig. 1. Temperature dependence of the energy of the PL maximum. PL spectra at 10 K and 300 K are shown in the inset.
maximum energy reveals the presence of localized states in the layer. At low temperatures, the PL emission comes from regions of the ordered clusters with the lowest potential, where the photogenerated carriers are localized. When the temperature increases, the carriers are thermalized to larger spatial regions, and therefore, the value of the PL maximum energy changes. For temperatures higher than 100 K, the emission comes from the entire volume of the ordered clusters and the temperature dependence of the PL maximum energy follows the Varshni formula that characterizes a uniform material. To characterize atomic ordering, the parameter 0 ≤ η ≤ 1 is usually used. For ternary alloys its value is equal to the increase or decrease in concentration of one of the elements (for example, Ga or In for the GaInP alloy) in the alternating monolayers rich or poor in this element. The value of this parameter is usually obtained from the value of bandgap reduction due to atomic ordering. We calculated the value of η by considering the PL maximum energy measured at room temperature and the band-gap reduction relative to the band gap of a disordered AlGaInP alloy with the same atomic composition taken from Ref. [2]. Using relation (1) from Ref. [13], we found that the value of η was approximately equal to 0.5, which is the maximum possible value in a GaInP alloy [14]. The value of biaxial strain, ε = (as – al)/al, where al and as are the lattice constants of the layer and the substrate, respectively, was obtained as ε = −0.001 from rocking curves measured by HRXRD. Besides, the measurements made by HRXRD provided evidence of the high atomic ordering in the AlGaInP layer: the ½ (115) superstructure reflection peak, which does not exist in a disordered structure, was detected.
3. Results and discussion To understand the nature of the radiative transitions, PL spectra of the AlGaInP alloy were measured without any polarization distinction in a temperature range from 10 to 300 K. Only one PL peak from the AlGaInP layer, with its maximum at 2.033 (2.087) eV at 300 (10) K, was observed. Fig. 1 shows that the temperature behavior of the energy at which the maximum of the PL peak occurs is S-shaped. At low temperatures, this energy decreases with increasing temperature and has a local minimum at 50 K; it then increases, reaches its maximum value at 100 K, and finally, after this temperature, decreases following the Varshni rule. At low excitation density, the S-shaped temperature dependence is commonly observed in layers with atomic ordering and also in nonhomogeneous materials with potential fluctuations. It is well known that semiconductor alloys with atomic ordering are not uniform, but contain ordered clusters, and present also a periodic variation of atomic content [10–12]. Therefore, the temperature dependence of the PL
3.1. Calculation of the angular dependence of the PL emission polarization The polarization of the PL emission depends on crystal symmetry. The symmetry reduction due to atomic ordering and biaxial strain splits the valence band maximum. The resulting energy difference between HH and LH valence subbands favors radiative transitions from the conduction band (CB) to the topmost of these subbands, and the symmetry of this topmost subband determines the polarization of the PL emission. We assumed parabolic bands and vertical transition rates equal to the k = 0 transition rates to find that the emitted PL intensity for a given polarization ϵ is proportional to
I (ϵ ) = μc*, hh3/2 γc, hh + μc*, lh3/2 γc, lh e−∆ Ehh, ll/ kB T + μc*, SO3/2 γc, SO e−∆ Ehh, SO/ kB T , where kB is the Boltzmann constant, T is the absolute temperature, and μ*c,vv, with vv = hh (heavy hole), lh (light hole),or SO (spin-orbit split-off 335
Journal of Luminescence 195 (2018) 334–338
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due to the explicit temperature dependence of the Boltzmann factor. The value of biaxial strain ε used in the calculations was obtained experimentally using the layer lattice parameter determined by HRXRD. The integrated PL intensities for each polarization were taken into account: In measurements, all the directions of the polarization vector contribute to the direction selected by the polarizer, thus to compare with the measured PL intensity, we consider the contribution of all polarizations to the intensity for a given polarizer direction, φ, by π 1 integrating the emission rate to obtain I (ϕ) = 2π ∫−π I (θ)cos2 (θ − ϕ)⋅dθ Fig. 2 shows calculation results for the polarization degree of the PL emission as a function of elastic strain, ε, for different values of the ordering parameter, η, and different temperatures. The polarization degree is defined as (Imax-Imin)/(Imax+Imin), where Imax and Imin are, respectively, maximum and minimum values of the integrated PL intensity in a given polarization pattern. When the ordering parameter is low (less than approximately 0.3), the polarization degree reaches its maximum value, at any temperature, when ε is close to zero, i.e., when the alloy has no elastic strain. In the presence of internal biaxial strain and for low values of the ordering parameter, the polarization degree decreases to almost zero and the higher the strain, the lower the polarization degree. When the ordering parameter is higher than approximately 0.35, the polarization degree is almost independent of the value of the strain and keeps a high value for any value of biaxial strain. At room temperature (Fig. 1a) and for a given constant value of the strain, the polarization degree increases with the ordering parameter. When the temperature decreases, the polarization degree increases for any value of the ordering parameter. At low temperatures, the maximum value of the polarization degree, in the absence of biaxial strain, is almost independent of the ordering parameter (see Fig. 1b). Within our calculation model, this could be explained as follows: The value of the polarization degree maximum is proportional to the value of the valence band splitting (VBS), which, in turn, depends on the ordering parameter. At low temperatures, the valence bands are narrower, and therefore, the radiative transitions from the conduction band to the lower lying LH valence subband hardly contribute to the PL emission intensity. Thus, at low temperatures, for any ordering parameter, the maximum of the polarization degree is close to the same value of approximately 0.25. As far as we can see, neither the consideration of the temperature
band hole), are the reduced effective masses, which, in terms of the effective mass m*c of conduction band electrons and the effective masses m*vv of valence band holes, are given by
μc*, vv =
mc*m vv* . mc* + m vv*
The factors γc, vv are related to the probabilities for the emission of photons with polarization vector ϵ due to vertical transitions at the center of the Brillouin zone (k = 0) from the states |ic of the conduction band to the states | jvv of one of the valence sub-bands. These factors are given by
γc, vv =
∑
jvv ϵ⋅p ic
2
,
i, j
where p is the linear momentum operator, and we calculated them using the procedure of Wei and Zunger [15] in which the effects of coexisting atomic ordering and biaxial strain on the valence-band edge states in ternary alloys are found using a six-state basis. It is worth mentioning that I(ϵ ) is proportional to the spontaneous emission rate of photons with polarization vector ϵ . The constant of proportionality contains the temperature dependent factor
(
(kB T )3/2exp −
Eg − ∆ F kB T
),
where ∆F /kB is the difference between the
Fermi temperatures of electrons and holes. Neglecting this factor in the calculations does not affect our conclusions since we normalize the calculated polarization patterns to compare to experimental results. Further, this factor cancels in the calculation of the polarization degree, as it may be seen from the definition given below. We used the expression for I(ϵ ) to calculate the PL intensity as a function of polarization angle for the PL emission propagating along the [001] crystallographic direction of the GaInP alloy. In the calculations, CuPt type atomic ordering and internal biaxial strain were taken into account. The lattice constant of the alloy was calculated using Vegard's law. Effective mass and lattice constant values for InP and GaP were taken from Ref. [16], and other material parameters from Ref. [15]. The value of the valence band splitting due to ordering for the completely ordered alloy was taken as 0.2 eV, and the band gap reduction due to ordering as 0.471 eV [13]. In the calculation of the PL intensity for different temperatures, we did not take into account the temperature variation of the material parameters and considered only the change
Fig. 2. Calculated PL emission polarization degree as a function of ordering parameter η and biaxial strain ε at (a) 300 K, (b) 10 K. The polarization degree is defined as (Imax-Imin)/ (Imax+Imin), where Imax and Imin are, respectively, maximum and minimum values of the integrated PL intensity in the polarization pattern obtained for each pair of values of η and ε.
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Fig. 3. Normalized measured (dots) and calculated (dashed curve) polarization patterns of the surface-emitted PL for the AlGaInP layer at different temperatures. The vertical (horizontal) axis corresponds to the [110] ([1–10]) crystallographic direction.
emitting regions changes with temperature. In Fig. 4b, the calculated dependence of the PL polarization degree as a function of strain at different temperatures is displayed. At room temperature, the layer is under compressive strain; then, if we suppose that strain decreases with decreasing temperature, the polarization degree has to increase, and it will reach its maximum value when the strain is close to zero; if the strain then becomes tensile, the polarization degree will decrease to values lower than that observed at 300 K. We showed recently [9] that the temperature behavior of the PL polarization degree of slightly ordered GaInAsP alloys can be explained by considering the change of elastic strain with temperature. Thus, a non-monotonic temperature behavior is consistent with the model, except for the too high experimental values of the polarization degree near its maximum (0.36). In our calculations for AlGaInP, we used the parameters of the GaInP alloy, since the values of band gap reduction and VBS of the totally ordered quaternary AlGaInP alloy have not been reported. Other parameters of AlGaInP, such as the effective masses and deformation potentials, can influence the value of the polarization degree. However, as the Al concentration in our alloy is low, we suppose that the AlGaInP parameters are close to those of Ga0.5In0.5P and, therefore, they would not give significantly different calculated values. However, there is another factor that has to be taken into consideration: the non-uniformity of an ordered layer. One can see that the temperature behavior of the PL polarization degree is similar to the temperature behavior of the PL energy maximum shown in Fig. 1. Both: the temperature dependence of the PL polarization and of the PL maximum energy, at room temperature, show values close to those predicted by the model, both reach their maxima at approximately 100 K, and then both have a significant decrease in disagreement with the models made for the uniform material. For the measurements of
change of other material parameters, nor the use of a more complicated model for the band-to-band transitions, can give results for the temperature dependence or the value of the polarization degree at low temperatures noticeably different from those obtained by our calculation model. 3.2. Measured angular dependence of the PL emission polarization In Fig. 3, polar plots of the PL polarized emission for different temperatures are shown for the AlGaInP alloy. There, the vertical (horizontal) axis corresponds to the [110] ([1–10]) crystallographic direction. Each point of the experimental curve corresponds to the integrated PL intensities, i.e., to the area under the corresponding PL peak for every PL polarization direction. Calculations for the AlGaInP quaternary alloy were made using the same model and the same parameters as for the GaInP ternary alloy. The values η = 0.5 and ε = −0.001 were used. The measured and calculated values of the polarization degree are compared in Fig. 4a. It can be seen there that, when the temperature decreases, the PL polarization degree of the highly ordered AlGaInP alloy first increases and reaches its maximum value of 0.36 at approximately 100 K. Then, at low temperatures, it decreases to values lower than those observed at room temperature. If we assume that biaxial strain remains constant when the temperature decreases, our calculation model predicts that the polarization degree increases monotonically with decreasing temperature, as it is shown in Fig. 4a (empty circles). The non-monotonic temperature dependence of the experimental PL polarization degree (Fig. 4a, solid triangles) could be explained within the frame of our model, if one considers that elastic biaxial strain in the
Fig. 4. a) Measured and calculated values of the PL emission polarization degree for different temperatures. The measured (calculated) values are plotted as solid triangles (empty squares). b) PL emission polarization degree as a function of biaxial elastic strain calculated for different temperatures using η = 0.5.
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Integrated Imaging Facility for help provided in the characterization of the structures. This research was partially supported by Grant No. 276 from VIEP-BUAP, Puebla, Mexico.
both dependences, the lowest possible values of excitation intensity were used. Within the explanation based on the assumption that the PL process at low temperatures is determined by the emission from spatial regions having the lowest potential, we have to assume that those regions are (or get) under tensile biaxial strain at low temperature. When the temperature increases, the excited carriers thermalize and occupy larger spatial regions; thus, when the PL emission comes from the entire ordered cluster, the temperature dependence follows the curve characteristic for the uniform material. On the other hand, the analysis of the polarization of the PL emission (or of the absorption by the ordered layer, which has to show the same temperature behavior) is giving information about the complex internal structure of ordered III-V layers. In fact, the study of the internal structure of the alloy and its relation to emission and absorption properties is important for attempting to enhance optical device performance. The polarized PL emission points to emitting regions with non-cubic crystal symmetry, and the low values of the PL polarization degree obtained at low temperature point to a complex non-uniform structure of the quaternary alloy.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jlumin.2017.11.016. References [1] Th Gessmann, E.F. Schubert, High-efficiency AlGaInP light-emitting diodes for solid-state lighting applications, J. Appl. Phys. 95 (2004) 2203–2216. [2] Y.-G. Zhang, Y. Gu, Al(Ga)InP-GaAs photodiodes tailored for specific wavelength range, in: I. Yun (Ed.), Photodiodes – From Fundamentals to Applications, InTech, 2012, pp. 261–287, , http://dx.doi.org/10.5772/50404 https://www.intechopen. com/books/photodiodes-from-fundamentals-to-applications/al-ga-inp-gaasphotodiodes-tailored-for-specific-wavelength-range. [3] A. Gomyo, T. Suzuki, K. Kobayashi, S. Kawata, I. Hino, T. Yuasa, Evidence for the existence of an ordered state in Ga0.5In0.5P grown by metalorganic vapor phase epitaxy and its relation to band-gap energy, Appl. Phys. Lett. 50 (1987) 673–675. [4] A. Mascarenhas, S. Kurtz, A. Kibbler, J.M. Olson, Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P, Phys. Rev. Lett. 63 (1989) 2108–2111. [5] K. Nakano, A. Toda, T. Yamamoto, A. Ishibashi, Effects of ordering on the operation of AlGaInP lasers grown by metalorganic chemical vapor deposition, Appl. Phys. Lett. 61 (1992) 1959–1961. [6] O.P. Kowalski, R.M. Wegerer, D.J. Mowbray, M.S. Skolnick, C.C. Button, J.S. Roberts, M. Hopkinson, J.P.R. David, G. Hill, Optical spectroscopic observation of spontaneous long range ordering in AlGaInP, Appl. Phys. Lett. 68 (1996) 3266–3268. [7] S.-H. Wei, A. Zunger, Optical properties of zinc-blende semiconductor alloys: effects of epitaxial strain and atomic ordering, Phys. Rev. B 49 (1994) 14337–14351. [8] T. Prutskij, G. Attolini, V. Lantratov, N. Kalyuzhnyy, Optical method of estimation of degree of atomic ordering within quaternary semiconductor alloys, J. Appl. Phys. 112 (2012) (023102–1-4). [9] T. Prutskij, N. Makarov, G. Attolini, Temperature dependence of the photoluminescence polarization of ordered III-V semiconductor alloys, J. Appl. Phys. 119 (2016) (115702–1-5). [10] D.M. Follstaedt, R.P. Schneider Jr, E.D. Jones, Microstructures of (In, Ga)P alloys grown on GaAs by metalorganic vapor-phase epitaxy, J. Appl. Phys. 77 (1995) 3077–3087. [11] A. Ponchet, A. Rocher, J.-Y. Emery, C. Starck, L. Goldstein, Lateral modulations in zero-net-strained GaInAsP multilayers grown by gas source molecular-beam epitaxy, J. Appl. Phys. 74 (1993) 3778–3782. [12] S. Smith, H.M. Cheong, B.D. Fluegel, J.F. Geisz, J.M. Olson, L.L. Kazmerski, A. Mascarenhas, Spatially resolved photoluminescence in partially ordered GaInP2, Appl. Phys. Lett. 74 (1999) 706–708. [13] P. Ernst, C. Geng, F. Scholz, H. Schweizer, Y. Zhang, A. Mascarehnas, Band-gap reduction and valence-band splitting of ordered GaInP2, Appl. Phys. Lett. 67 (1995) 2347–2349. [14] O. Pagès, A. Chafi, D. Fristot, A.V. Postnikov, (Ga, In)P: a standard alloy in the classification of phonon mode behavior, Phys. Rev. B 73 (2006) (165206–1-10). [15] S.-H. Wei, A. Zunger, Strain effects on the spectra of spontaneously ordered GaxIn1− xP, Appl. Phys. Lett. 64 (1994) 757–759. [16] S. Adachi, Material parameters of In1− xGaxAsy P1− y and related binaries, J. Appl. Phys. 53 (1982) 8775–8792.
4. Conclusions Measured and calculated angular dependences of the PL emission from the (001) surface plane of a quaternary AlGaInP epitaxial alloy grown on a GaAs substrate using MOVPE were compared at different temperatures. Calculations were made using a model which takes into account the coexistence of CuPt atomic ordering and elastic biaxial strain in a ternary semiconductor alloy. At room temperature, the measured and calculated polarization degrees of the PL emission from AlGaInP layers are close to each other; while at low temperatures, these values are different. The PL emission polarization increases when the temperature decreases from 300 to 100 K, goes through a local maximum at a temperature close to 100 K, and then, at low temperatures, instead of increasing, as the calculation predicts, the PL polarization decreases notably, reaching values close to zero. This temperature behavior could be explained within the model, if an assumed appropriate change of elastic strain is taken into account. It is well known that ordered III-V semiconductor alloys are never uniform but have a complex internal structure. Thus, we relate this temperature behavior of the polarization degree to the change of local elastic strain in the spatial regions participating in the radiative recombination at low temperatures. Acknowledgments The authors gratefully acknowledge the Notre Dame University
338
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
The effect of temperature on the linear polarization of the photoluminescence of an ordered AlGaInP semiconductor alloy
T
⁎
T. Prutskija, , P. Seredinb, G. Attolinic a
Instituto de Ciencias, BUAP, Privada 17 Norte No. 3417, Col. San Miguel Hueyotlipan, 72050 Puebla, Pue., Mexico Voronezh State University, Universitetskaya pl., 1, 394006 Voronezh, Russia c IMEM/CNR, Parco Area delle Scienze 37/A, 43010 Parma, Italy b
A B S T R A C T The photoluminescence (PL) emission of atomically ordered III-V epitaxial alloys grown by MOVPE is frequently polarized. We analyze the linear polarization of the PL emission from the (001) surface of an epitaxial semiconductor quaternary AlGaInP alloy with high atomic ordering parameter. We measured and calculated the temperature dependence of the PL polarization for a wide temperature range (10–300 K). Comparing the measured polarization patterns with patterns calculated using constant values of the atomic ordering and elastic biaxial strain parameters, we found that the calculations do not predict correctly the PL polarization patterns at low temperature. Furthermore, our measurements show that at room temperature the measured and calculated PL polarization degrees are almost the same, while at low temperature the measured values are smaller than those predicted by the model used for the calculations. We discuss the factors that could cause this discrepancy and conclude that it can be attributed to the complex internal structure of the layer.
1. Introduction The quaternary (AlxGa1−x)0.5In0.5P alloy is an important III-V material almost lattice matched to GaAs for any value of x and suitable for fabrication of optoelectronic devices working in the red, orange, and yellow wavelength range [1,2] For values of x greater than 0.52 the alloy becomes an indirect-gap semiconductor, and thus, the (AlxGa1−x)0.5In0.5P alloy with x =0.52 is the III-V alloy with the largest direct bandgap and lattice-matched to GaAs substrates. It is well known that in ternary and quaternary III-V alloys grown by metal-organic vapor phase epitaxy (MOVPE) atomically ordered clusters are spontaneously formed during the growth process [3,4]. Atomically ordered IIIV ternary alloys have a superstructure in which monolayers rich in one of the group III (or group V) elements alternate with monolayers rich in the other element of the same group present in the alloy. In the GaInP alloy, for example, the atomically ordered structure consists of a superlattice structure made of alternate In-rich and Ga-rich {111} diagonal planes, with interleaving planes of P atoms, corresponding to the CuPt type of ordering. Since the difference between the covalent radius of the Al and Ga atoms is small, the structural, elastic, and electronic characteristics of the AlInP and GaInP alloys are similar. It has been shown that atomic ordering of the same CuPt type also occurs in (AlxGa1−x)0.5In0.5P quaternary alloys grown by MOVPE [5,6]
⁎
coexisting with biaxial strain due to the difference between the lattice constants of the epitaxial layer and the substrate. Atomic ordering changes the cubic symmetry of the disordered III-V alloy and splits the valence band maximum, separating the heavy-hole (HH) and light-hole (LH) valence bands at the center of the Brillouin zone [4,7]; as a result of this crystal symmetry transformation, the PL emission of the alloy becomes polarized. Additionally, the mismatch between the substrate and epitaxial-layer lattice constants causes a deformation of the layer crystal lattice, and leads to the presence of elastic biaxial strain in the layer. Strain also changes the crystal symmetry and influences the polarization of the PL emission. In previous works, we have made approximate calculations to find the polarization of the PL emitted by ordered III-V alloys [8,9]. In these calculations, parabolic bands and vertical transition rates equal to k = 0 transition rates were assumed to calculate, the polarization of the PL emission propagating along any crystallographic axis for different values of the parameters of ordering and biaxial strain. We used the same approximations in this work to calculate also the effect of temperature on the PL polarization. Here, we analyze the temperature dependence of the polarization of the PL emission of a highly ordered epitaxial layer of Al0.14Ga0.37In0.49P alloy grown by MOVPE on a (001)-oriented GaAs substrate. We measured and calculated the degree of polarization of the PL emission from
Correspondence to: Departamento de Fisicoquimica de Materiales, Instituto de Ciencias, Privada 17 Norte, No 3417, Col. San Miguel Huyeotlipan, 72050 Puebla, Pue., Mexico. E-mail addresses: [email protected] (T. Prutskij), [email protected] (P. Seredin).
https://doi.org/10.1016/j.jlumin.2017.11.016 Received 28 June 2017; Received in revised form 9 November 2017; Accepted 13 November 2017 Available online 21 November 2017 0022-2313/ © 2017 Elsevier B.V. All rights reserved.
Journal of Luminescence 195 (2018) 334–338
T. Prutskij et al.
the (001) surface of this layer at different temperatures, and we analyzed the temperature behavior of the PL emission. In contrast with the calculations, the experimentally found PL polarization degree has a non-monotonic temperature dependence. We discuss here the reasons that could lead to this discrepancy. To the best of our knowledge, this is the first study of the temperature dependence of the polarization of the PL emission from the (001) surface of a III-V semiconductor alloy with high atomic ordering. 2. Material and methods The Al0.14Ga0.37In0.49P epitaxial layer was grown on a (001) GaAs substrate at 725 °C by the MOVPE technique in a horizontal reactor with a rotating wafer susceptor. A 300-nm-thick GaAs buffer layer was grown before the Al0.14Ga0.37In0.49P layer deposition. Trimethylaluminium, trimethylgallium, and trimethylindium were used as group-III sources, and phosphine as group-V precursor. The molar ratio V/III in the gas phase was of 80, the growth rate was of 5 Å/s, and the layer thickness was approximately of 0.5 µm. After the growth of the layer was complete, the layer surface morphology was examined by scanning electron microscopy, the layer atomic content was measured by Energy-Dispersive X-ray Spectroscopy (EDS), and the mismatch between the layer and substrate lattices was determined from rocking curves measured by high-resolution X-ray diffraction (HRXRD). The temperature dependence of the linear polarization of the PL emission was measured within the temperature range from 10 to 300 K. A conventional experimental set-up, including a close-cycle He cryostat, a TRIAX550 monochromator, and a liquid-nitrogen-cooled chargecoupled-device detector, was used for measuring the PL emission from the surface of the layer. Optical excitation for PL was provided by a solid state laser with a wavelength of 532 nm. To measure the PL polarization, a quartz depolarizer and a rotating linear polarizer were mounted before the sample surface. Thus, the exciting laser beam was depolarized and then linearly polarized before focusing on the sample surface, and the PL emission was collected by the same objective, after having passed through the same polarizer and depolarizer as the incident beam. Therefore, we detected the light polarized along the same direction as the exciting beam. To avoid the polarization due to the monochromator grating, another depolarizer was installed at the entrance slit of the monochromator. The diameter of the laser spot on the sample surface was of about 2 mm, and the lowest possible excitation intensity, of approximately 1–3 mW, over all the area, was used. To obtain the integrated intensity of the PL emission from the surface of the layer, the area under the corresponding PL peak was calculated by integration of the PL curve. In what follows, Al0.14Ga0.37In0.49P will be abbreviated as AlGaInP.
Fig. 1. Temperature dependence of the energy of the PL maximum. PL spectra at 10 K and 300 K are shown in the inset.
maximum energy reveals the presence of localized states in the layer. At low temperatures, the PL emission comes from regions of the ordered clusters with the lowest potential, where the photogenerated carriers are localized. When the temperature increases, the carriers are thermalized to larger spatial regions, and therefore, the value of the PL maximum energy changes. For temperatures higher than 100 K, the emission comes from the entire volume of the ordered clusters and the temperature dependence of the PL maximum energy follows the Varshni formula that characterizes a uniform material. To characterize atomic ordering, the parameter 0 ≤ η ≤ 1 is usually used. For ternary alloys its value is equal to the increase or decrease in concentration of one of the elements (for example, Ga or In for the GaInP alloy) in the alternating monolayers rich or poor in this element. The value of this parameter is usually obtained from the value of bandgap reduction due to atomic ordering. We calculated the value of η by considering the PL maximum energy measured at room temperature and the band-gap reduction relative to the band gap of a disordered AlGaInP alloy with the same atomic composition taken from Ref. [2]. Using relation (1) from Ref. [13], we found that the value of η was approximately equal to 0.5, which is the maximum possible value in a GaInP alloy [14]. The value of biaxial strain, ε = (as – al)/al, where al and as are the lattice constants of the layer and the substrate, respectively, was obtained as ε = −0.001 from rocking curves measured by HRXRD. Besides, the measurements made by HRXRD provided evidence of the high atomic ordering in the AlGaInP layer: the ½ (115) superstructure reflection peak, which does not exist in a disordered structure, was detected.
3. Results and discussion To understand the nature of the radiative transitions, PL spectra of the AlGaInP alloy were measured without any polarization distinction in a temperature range from 10 to 300 K. Only one PL peak from the AlGaInP layer, with its maximum at 2.033 (2.087) eV at 300 (10) K, was observed. Fig. 1 shows that the temperature behavior of the energy at which the maximum of the PL peak occurs is S-shaped. At low temperatures, this energy decreases with increasing temperature and has a local minimum at 50 K; it then increases, reaches its maximum value at 100 K, and finally, after this temperature, decreases following the Varshni rule. At low excitation density, the S-shaped temperature dependence is commonly observed in layers with atomic ordering and also in nonhomogeneous materials with potential fluctuations. It is well known that semiconductor alloys with atomic ordering are not uniform, but contain ordered clusters, and present also a periodic variation of atomic content [10–12]. Therefore, the temperature dependence of the PL
3.1. Calculation of the angular dependence of the PL emission polarization The polarization of the PL emission depends on crystal symmetry. The symmetry reduction due to atomic ordering and biaxial strain splits the valence band maximum. The resulting energy difference between HH and LH valence subbands favors radiative transitions from the conduction band (CB) to the topmost of these subbands, and the symmetry of this topmost subband determines the polarization of the PL emission. We assumed parabolic bands and vertical transition rates equal to the k = 0 transition rates to find that the emitted PL intensity for a given polarization ϵ is proportional to
I (ϵ ) = μc*, hh3/2 γc, hh + μc*, lh3/2 γc, lh e−∆ Ehh, ll/ kB T + μc*, SO3/2 γc, SO e−∆ Ehh, SO/ kB T , where kB is the Boltzmann constant, T is the absolute temperature, and μ*c,vv, with vv = hh (heavy hole), lh (light hole),or SO (spin-orbit split-off 335
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due to the explicit temperature dependence of the Boltzmann factor. The value of biaxial strain ε used in the calculations was obtained experimentally using the layer lattice parameter determined by HRXRD. The integrated PL intensities for each polarization were taken into account: In measurements, all the directions of the polarization vector contribute to the direction selected by the polarizer, thus to compare with the measured PL intensity, we consider the contribution of all polarizations to the intensity for a given polarizer direction, φ, by π 1 integrating the emission rate to obtain I (ϕ) = 2π ∫−π I (θ)cos2 (θ − ϕ)⋅dθ Fig. 2 shows calculation results for the polarization degree of the PL emission as a function of elastic strain, ε, for different values of the ordering parameter, η, and different temperatures. The polarization degree is defined as (Imax-Imin)/(Imax+Imin), where Imax and Imin are, respectively, maximum and minimum values of the integrated PL intensity in a given polarization pattern. When the ordering parameter is low (less than approximately 0.3), the polarization degree reaches its maximum value, at any temperature, when ε is close to zero, i.e., when the alloy has no elastic strain. In the presence of internal biaxial strain and for low values of the ordering parameter, the polarization degree decreases to almost zero and the higher the strain, the lower the polarization degree. When the ordering parameter is higher than approximately 0.35, the polarization degree is almost independent of the value of the strain and keeps a high value for any value of biaxial strain. At room temperature (Fig. 1a) and for a given constant value of the strain, the polarization degree increases with the ordering parameter. When the temperature decreases, the polarization degree increases for any value of the ordering parameter. At low temperatures, the maximum value of the polarization degree, in the absence of biaxial strain, is almost independent of the ordering parameter (see Fig. 1b). Within our calculation model, this could be explained as follows: The value of the polarization degree maximum is proportional to the value of the valence band splitting (VBS), which, in turn, depends on the ordering parameter. At low temperatures, the valence bands are narrower, and therefore, the radiative transitions from the conduction band to the lower lying LH valence subband hardly contribute to the PL emission intensity. Thus, at low temperatures, for any ordering parameter, the maximum of the polarization degree is close to the same value of approximately 0.25. As far as we can see, neither the consideration of the temperature
band hole), are the reduced effective masses, which, in terms of the effective mass m*c of conduction band electrons and the effective masses m*vv of valence band holes, are given by
μc*, vv =
mc*m vv* . mc* + m vv*
The factors γc, vv are related to the probabilities for the emission of photons with polarization vector ϵ due to vertical transitions at the center of the Brillouin zone (k = 0) from the states |ic of the conduction band to the states | jvv of one of the valence sub-bands. These factors are given by
γc, vv =
∑
jvv ϵ⋅p ic
2
,
i, j
where p is the linear momentum operator, and we calculated them using the procedure of Wei and Zunger [15] in which the effects of coexisting atomic ordering and biaxial strain on the valence-band edge states in ternary alloys are found using a six-state basis. It is worth mentioning that I(ϵ ) is proportional to the spontaneous emission rate of photons with polarization vector ϵ . The constant of proportionality contains the temperature dependent factor
(
(kB T )3/2exp −
Eg − ∆ F kB T
),
where ∆F /kB is the difference between the
Fermi temperatures of electrons and holes. Neglecting this factor in the calculations does not affect our conclusions since we normalize the calculated polarization patterns to compare to experimental results. Further, this factor cancels in the calculation of the polarization degree, as it may be seen from the definition given below. We used the expression for I(ϵ ) to calculate the PL intensity as a function of polarization angle for the PL emission propagating along the [001] crystallographic direction of the GaInP alloy. In the calculations, CuPt type atomic ordering and internal biaxial strain were taken into account. The lattice constant of the alloy was calculated using Vegard's law. Effective mass and lattice constant values for InP and GaP were taken from Ref. [16], and other material parameters from Ref. [15]. The value of the valence band splitting due to ordering for the completely ordered alloy was taken as 0.2 eV, and the band gap reduction due to ordering as 0.471 eV [13]. In the calculation of the PL intensity for different temperatures, we did not take into account the temperature variation of the material parameters and considered only the change
Fig. 2. Calculated PL emission polarization degree as a function of ordering parameter η and biaxial strain ε at (a) 300 K, (b) 10 K. The polarization degree is defined as (Imax-Imin)/ (Imax+Imin), where Imax and Imin are, respectively, maximum and minimum values of the integrated PL intensity in the polarization pattern obtained for each pair of values of η and ε.
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Fig. 3. Normalized measured (dots) and calculated (dashed curve) polarization patterns of the surface-emitted PL for the AlGaInP layer at different temperatures. The vertical (horizontal) axis corresponds to the [110] ([1–10]) crystallographic direction.
emitting regions changes with temperature. In Fig. 4b, the calculated dependence of the PL polarization degree as a function of strain at different temperatures is displayed. At room temperature, the layer is under compressive strain; then, if we suppose that strain decreases with decreasing temperature, the polarization degree has to increase, and it will reach its maximum value when the strain is close to zero; if the strain then becomes tensile, the polarization degree will decrease to values lower than that observed at 300 K. We showed recently [9] that the temperature behavior of the PL polarization degree of slightly ordered GaInAsP alloys can be explained by considering the change of elastic strain with temperature. Thus, a non-monotonic temperature behavior is consistent with the model, except for the too high experimental values of the polarization degree near its maximum (0.36). In our calculations for AlGaInP, we used the parameters of the GaInP alloy, since the values of band gap reduction and VBS of the totally ordered quaternary AlGaInP alloy have not been reported. Other parameters of AlGaInP, such as the effective masses and deformation potentials, can influence the value of the polarization degree. However, as the Al concentration in our alloy is low, we suppose that the AlGaInP parameters are close to those of Ga0.5In0.5P and, therefore, they would not give significantly different calculated values. However, there is another factor that has to be taken into consideration: the non-uniformity of an ordered layer. One can see that the temperature behavior of the PL polarization degree is similar to the temperature behavior of the PL energy maximum shown in Fig. 1. Both: the temperature dependence of the PL polarization and of the PL maximum energy, at room temperature, show values close to those predicted by the model, both reach their maxima at approximately 100 K, and then both have a significant decrease in disagreement with the models made for the uniform material. For the measurements of
change of other material parameters, nor the use of a more complicated model for the band-to-band transitions, can give results for the temperature dependence or the value of the polarization degree at low temperatures noticeably different from those obtained by our calculation model. 3.2. Measured angular dependence of the PL emission polarization In Fig. 3, polar plots of the PL polarized emission for different temperatures are shown for the AlGaInP alloy. There, the vertical (horizontal) axis corresponds to the [110] ([1–10]) crystallographic direction. Each point of the experimental curve corresponds to the integrated PL intensities, i.e., to the area under the corresponding PL peak for every PL polarization direction. Calculations for the AlGaInP quaternary alloy were made using the same model and the same parameters as for the GaInP ternary alloy. The values η = 0.5 and ε = −0.001 were used. The measured and calculated values of the polarization degree are compared in Fig. 4a. It can be seen there that, when the temperature decreases, the PL polarization degree of the highly ordered AlGaInP alloy first increases and reaches its maximum value of 0.36 at approximately 100 K. Then, at low temperatures, it decreases to values lower than those observed at room temperature. If we assume that biaxial strain remains constant when the temperature decreases, our calculation model predicts that the polarization degree increases monotonically with decreasing temperature, as it is shown in Fig. 4a (empty circles). The non-monotonic temperature dependence of the experimental PL polarization degree (Fig. 4a, solid triangles) could be explained within the frame of our model, if one considers that elastic biaxial strain in the
Fig. 4. a) Measured and calculated values of the PL emission polarization degree for different temperatures. The measured (calculated) values are plotted as solid triangles (empty squares). b) PL emission polarization degree as a function of biaxial elastic strain calculated for different temperatures using η = 0.5.
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Integrated Imaging Facility for help provided in the characterization of the structures. This research was partially supported by Grant No. 276 from VIEP-BUAP, Puebla, Mexico.
both dependences, the lowest possible values of excitation intensity were used. Within the explanation based on the assumption that the PL process at low temperatures is determined by the emission from spatial regions having the lowest potential, we have to assume that those regions are (or get) under tensile biaxial strain at low temperature. When the temperature increases, the excited carriers thermalize and occupy larger spatial regions; thus, when the PL emission comes from the entire ordered cluster, the temperature dependence follows the curve characteristic for the uniform material. On the other hand, the analysis of the polarization of the PL emission (or of the absorption by the ordered layer, which has to show the same temperature behavior) is giving information about the complex internal structure of ordered III-V layers. In fact, the study of the internal structure of the alloy and its relation to emission and absorption properties is important for attempting to enhance optical device performance. The polarized PL emission points to emitting regions with non-cubic crystal symmetry, and the low values of the PL polarization degree obtained at low temperature point to a complex non-uniform structure of the quaternary alloy.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jlumin.2017.11.016. References [1] Th Gessmann, E.F. Schubert, High-efficiency AlGaInP light-emitting diodes for solid-state lighting applications, J. Appl. Phys. 95 (2004) 2203–2216. [2] Y.-G. Zhang, Y. Gu, Al(Ga)InP-GaAs photodiodes tailored for specific wavelength range, in: I. Yun (Ed.), Photodiodes – From Fundamentals to Applications, InTech, 2012, pp. 261–287, , http://dx.doi.org/10.5772/50404 https://www.intechopen. com/books/photodiodes-from-fundamentals-to-applications/al-ga-inp-gaasphotodiodes-tailored-for-specific-wavelength-range. [3] A. Gomyo, T. Suzuki, K. Kobayashi, S. Kawata, I. Hino, T. Yuasa, Evidence for the existence of an ordered state in Ga0.5In0.5P grown by metalorganic vapor phase epitaxy and its relation to band-gap energy, Appl. Phys. Lett. 50 (1987) 673–675. [4] A. Mascarenhas, S. Kurtz, A. Kibbler, J.M. Olson, Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P, Phys. Rev. Lett. 63 (1989) 2108–2111. [5] K. Nakano, A. Toda, T. Yamamoto, A. Ishibashi, Effects of ordering on the operation of AlGaInP lasers grown by metalorganic chemical vapor deposition, Appl. Phys. Lett. 61 (1992) 1959–1961. [6] O.P. Kowalski, R.M. Wegerer, D.J. Mowbray, M.S. Skolnick, C.C. Button, J.S. Roberts, M. Hopkinson, J.P.R. David, G. Hill, Optical spectroscopic observation of spontaneous long range ordering in AlGaInP, Appl. Phys. Lett. 68 (1996) 3266–3268. [7] S.-H. Wei, A. Zunger, Optical properties of zinc-blende semiconductor alloys: effects of epitaxial strain and atomic ordering, Phys. Rev. B 49 (1994) 14337–14351. [8] T. Prutskij, G. Attolini, V. Lantratov, N. Kalyuzhnyy, Optical method of estimation of degree of atomic ordering within quaternary semiconductor alloys, J. Appl. Phys. 112 (2012) (023102–1-4). [9] T. Prutskij, N. Makarov, G. Attolini, Temperature dependence of the photoluminescence polarization of ordered III-V semiconductor alloys, J. Appl. Phys. 119 (2016) (115702–1-5). [10] D.M. Follstaedt, R.P. Schneider Jr, E.D. Jones, Microstructures of (In, Ga)P alloys grown on GaAs by metalorganic vapor-phase epitaxy, J. Appl. Phys. 77 (1995) 3077–3087. [11] A. Ponchet, A. Rocher, J.-Y. Emery, C. Starck, L. Goldstein, Lateral modulations in zero-net-strained GaInAsP multilayers grown by gas source molecular-beam epitaxy, J. Appl. Phys. 74 (1993) 3778–3782. [12] S. Smith, H.M. Cheong, B.D. Fluegel, J.F. Geisz, J.M. Olson, L.L. Kazmerski, A. Mascarenhas, Spatially resolved photoluminescence in partially ordered GaInP2, Appl. Phys. Lett. 74 (1999) 706–708. [13] P. Ernst, C. Geng, F. Scholz, H. Schweizer, Y. Zhang, A. Mascarehnas, Band-gap reduction and valence-band splitting of ordered GaInP2, Appl. Phys. Lett. 67 (1995) 2347–2349. [14] O. Pagès, A. Chafi, D. Fristot, A.V. Postnikov, (Ga, In)P: a standard alloy in the classification of phonon mode behavior, Phys. Rev. B 73 (2006) (165206–1-10). [15] S.-H. Wei, A. Zunger, Strain effects on the spectra of spontaneously ordered GaxIn1− xP, Appl. Phys. Lett. 64 (1994) 757–759. [16] S. Adachi, Material parameters of In1− xGaxAsy P1− y and related binaries, J. Appl. Phys. 53 (1982) 8775–8792.
4. Conclusions Measured and calculated angular dependences of the PL emission from the (001) surface plane of a quaternary AlGaInP epitaxial alloy grown on a GaAs substrate using MOVPE were compared at different temperatures. Calculations were made using a model which takes into account the coexistence of CuPt atomic ordering and elastic biaxial strain in a ternary semiconductor alloy. At room temperature, the measured and calculated polarization degrees of the PL emission from AlGaInP layers are close to each other; while at low temperatures, these values are different. The PL emission polarization increases when the temperature decreases from 300 to 100 K, goes through a local maximum at a temperature close to 100 K, and then, at low temperatures, instead of increasing, as the calculation predicts, the PL polarization decreases notably, reaching values close to zero. This temperature behavior could be explained within the model, if an assumed appropriate change of elastic strain is taken into account. It is well known that ordered III-V semiconductor alloys are never uniform but have a complex internal structure. Thus, we relate this temperature behavior of the polarization degree to the change of local elastic strain in the spatial regions participating in the radiative recombination at low temperatures. Acknowledgments The authors gratefully acknowledge the Notre Dame University
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