Ga(NAs) double quantum wells

Journal of Luminescence 175 (2016) 255–259

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Charge transfer luminescence in (GaIn)As/GaAs/Ga(NAs) double quantum wells P. Springer a,n, S. Gies a, P. Hens a, C. Fuchs a, H. Han a, J. Hader b,c, J.V. Moloney b,c, W. Stolz a, K. Volz a, S.W. Koch a, W. Heimbrodt a a

Department of Physics and Material Sciences Center, Philipps-Universität Marburg, Renthof 5, 35032 Marburg, Germany Nonlinear Control Strategies Inc, 7040 N. Montecatina Dr., Tucson, AZ 85704, USA c College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA b

art ic l e i nf o

a b s t r a c t

Article history: Received 23 December 2015 Received in revised form 7 March 2016 Accepted 10 March 2016 Available online 18 March 2016

Charge transfer excitons are studied in double quantum well structures consisting of a (GaIn)As and a Ga (NAs) layer separated by a GaAs film of variable thickness. With decreasing barrier thickness, the gradual change from a spatially direct exciton within the (GaIn)As well to a charge transfer exciton bound across the GaAs spacing layer is observed. The optical spectra are well reproduced by a fully microscopic theory and band structure calculations based on the k
p method using a weak type-I valence band offset of approximately ð45 7 40Þ meV at the Ga(NAs)/GaAs interface. & 2016 Elsevier B.V. All rights reserved.

Keywords: Dilute nitrides Optical properties Photoluminescence Band structure Band offset

1. Introduction Luminescence properties of semiconductors are closely related to their inherent band structure and more specifically, the fundamental gap energy. Consequently, extending the toolset for band edge engineering of semiconductors always has been an important research subject. The demand to achieve, e.g., laser materials with specified operating wavelengths drives the search for methods that extends the flexibility of composition and strain control. The unusual bowing of the fundamental band gap in III–N–Vsemiconductor compounds has been established as a well suited tool for band gap engineering. It is already decreased by approximately 150 meV in Ga(NAs) alloys containing only 1% N [1–3]. This exceptional reduction has been described successfully in the framework of the band anticrossing (BAC) model, which leads to a shift of the conduction band edge due to the interaction of the localized impurity states with those of the conduction band edge [4]. The system has been studied experimentally and theoretically for more than a decade and a variety of applications in optoelectronic or photonic devices have been suggested [5]. Although the correlation of band gap shrinkage and N concentration is well known, the band n

Corresponding author. Tel.: +49 6421 28 24217; fax: +49 6421 28 27076. E-mail address: [email protected] (P. Springer).

http://dx.doi.org/10.1016/j.jlumin.2016.03.010 0022-2313/& 2016 Elsevier B.V. All rights reserved.

alignment of Ga(NAs)/GaAs heterostructures remains a subject of discussion. Even for similar strain states, both positive and negative valence band offsets have been reported [6–8]. In this paper, we present a quantum well (QW) heterostructure system that was designed to show a charge transfer (CT) photoluminescence (PL). This allows us to determine a precise value of the valence band offset (VBO) at the Ga(NAs)/GaAs interface by comparing the experimental spectra to those theoretically obtained using a fully microscopic theory. In Section 2, we discuss the growth and measurement related details. The theoretical description on band structure and PL calculations is given in Section 3. A discussion based on an experiment– theory comparison is presented in Section 4 and our studies are concluded in Section 5.

2. Experimental details The samples were grown in a commercial AIXTRON AIX 200 GFR (Gas Foil Rotation) metal organic vapor phase epitaxy (MOVPE) reactor system. While the standard group-III precursors triethylgallium (TEGa) and trimethylindium (TMIn) were used for the epitaxial growth, unsymmetrical dimethylhydrazine (UDMHy) and the arsenic precursor tertiarybutylarsine (TBAs) were used as group-V precursors. The reactor pressure was set to 50 mbar with H2 as carrier gas. A TBAs-stabilized bake-out procedure was

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exceeding 400 W cm  2 , a pulsed and frequency-doubled Nd:YAG laser at 532 nm with a repetition rate of 10 Hz and a temporal width of 3 ns was used. Here, the detection was done using a 0.25 m grating spectrometer and a InP/(InGa)(AsP) photomultiplier tube.

3. Theory To calculate the PL spectra of semiconductor heterostructures, we employ a completely microscopic theory based on the semiconductor luminescence equations (SLE). Besides the noninteracting parts, the system Hamiltonian includes the electron– electron and electron–phonon interactions [9–11]. Their scattering is described at the level of the second-Born approximation [12,13] to truncate the well known hierarchy problem. We evaluate the Fig. 1. Comparison of the experimental HR-XRD pattern in (004)—reflection (red) and the correspondent simulation (black) for the sample with a GaAs intermediate layer thickness of d ¼ 5:5 nm. The simulation is scaled by a factor of 10  1 for better visibility. The inset shows the respective TEM dark field image ðg ¼ ð002ÞÞ of the active region, which is repeated five times. While the QW layers were grown using the same growth conditions, the GaAs interlayer thickness was varied systematically. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1 Sample series specification. All parameters were attempted to be identical except the spacing layer thickness d. xIn

xN

dIn

dN

d

24.2% 24.1% 23.9%

4.9% 4.5% 4.6%

9.8 nm 9.8 nm 9.9 nm

4.0 nm 4.0 nm 4.0 nm

5.5 nm 2.5 nm 0.7 nm

applied in order to remove the native oxide layer from the GaAs (001) ð 7 0:11Þ substrate surface. The active region of the samples investigated in this study consists of a (GaIn)As QW, a GaAs intermediate layer, and a Ga (NAs) QW. The resulting double QW (DQW) was arranged as a 5 multiple QW-heterostructure (MQW-H) separated by 50 nm GaAs barriers. The growth temperature was chosen to be 525 °C. While the thickness of the QWs and the barrier remained constant, the layer thickness of the GaAs intermediate layer was varied systematically. The structural characterization of the samples was carried out using high resolution X-ray diffraction (HR-XRD, (004)-reflection). Thus, it was possible to evaluate layer thicknesses as well as alloy compositions of each of the layers described above by a full dynamical simulation of the experimental HR-XRD pattern. An example of such an evaluation is illustrated for the sample with an intermediate GaAs layer of 5.5 nm in Fig. 1. The alloy compositions xIn and xN as well as the layer thicknesses dIn and dN of the (GaIn) As and Ga(NAs) QW, respectively, are summarized together with the respective GaAs intermediate layer thickness d in Table 1. In order to verify this data, transmission electron microscopy (TEM) was used. The samples were prepared conventionally using Ar-ion-milling as last preparation step. Dark field images ðg ¼ ð002ÞÞ were taken using a JEOL 3010 transmission electron microscope with an acceleration voltage of 300 kV. This investigation reveals well defined and separated QWs as illustrated in the inset of Fig. 1 and confirms the HR-XRD data. We measured the PL using a standard setup. A frequencydoubled, diode-pumped solid state laser excited the samples at 532 nm. The laser was chopped mechanically to detect the signal by the lock-in technique via a 0.5 nm grating spectrometer and a liquid-nitrogen cooled germanium detector. For excitation powers

λ;ν

Heisenberg equation for the photon-assisted polarization Π k J ;q ¼
 † Δ b^ q a^ †λ;k J a^ ν;k J and the photon-number-like correlation N q ¼
 † Δ b^ q b^ q , consisting of creation (annihilation) operators of pho† ^ and electrons a^ † ðaÞ, ^ yielding [14] tons b^ ðbÞ 2 3 X   ∂ λ; ν PL ωq ¼ N q ¼ 2 Re4 ðF λq;ν Þ⋆ Π k J ;q 5; ∂t λ;ν;k

ð1Þ

J

  λ; ν ∂ λ; ν λ;ν iℏ Π k J ;q ¼ ϵ~ λ;k J  ϵ~ ν;k J  ℏωq Π k J ;q þ Ωq;k J ∂t   e h ;ν  1  f ν;k J f λ;k J U λq;k ; J

ð2Þ

which contains the stimulated (spontaneous) emission source term U (Ω), the renormalized single-particle energies ϵ~ , the eðhÞ , the light mode ωq ¼ c0 j qj , and electron (hole) distributions f the coupling matrix element F . While k J refers to the in-plane carrier momentum and q to the photonic wave vector, the subband indices are labeled λ and ν. The carrier distributions are assumed in thermal quasi-equilibrium, thus following Fermi–Dirac P e=h statistics. The carrier density is given by ne=h ¼ k J ;λ f λ;k J with ne ¼ nh  n. Structural disorder effects such as growth related variation of the band gap or layer thicknesses cause inhomogenous broadening. To account for these effects phenomenologically, we convolve the PL spectra by a Gaussian distribution characterized by its full width at half maximum (FWHM) Δ [13]. We retrieve the single-particle energies by diagonalizing the Luttinger–Hamiltonian containing the lowest conduction (e), heavy- (hh), and light-hole (lh), as well as split-off (so) band, each twice spin degenerate [15]. The envelope function approach [16,17] is applied to obtain the QW band structure. Subbands arising from confined electrons are labeled according to the respective band and their energetic order therein. Besides effects due to epitaxial strain which we treat in the Bir–Pikus formalism [18–20], this model fully accounts for interactions between all bands. The bulk 8  8 Hamiltonian is further extended to appropriately describe the near band gap states using a BAC model [4,6,21], which has been very successful in describing the band gap bowing of diluted semiconductors. Within this model, the conduction band edge energy Ecb of the diluted material at the zonecenter is parameterized according to ! chost 12 ϵ 1  ð3Þ Ecb ¼ Egap þ 2ahost  ΔEcb ; xx c chost 11 containing the band gap Egap , elastic constants chost and chost 11 12 , hydrostatic deformation potential ac , and conduction band offset

P. Springer et al. / Journal of Luminescence 175 (2016) 255–259

Fig. 2. Sketch of the sample series showing the most relevant electron and hole wave functions and transitions. The central GaAs spacing layer thickness d is varied within the different samples. The conduction and heavy-hole bands are shown as solid lines, while the light-hole band is shown as a dotted line.

ΔEcb . The lattice mismatched strain is given by a a ϵxx ¼ s ; a

ð4Þ

where as is the substrate and a the material lattice constant. The superscript host indicates that all material parameters such as effective masses are interpolated exclusively using the host values, with the only exception being the lattice constant [22]. Similarly, the dispersion-free defect band associated with the localized nitrogen impurities reads ! chost N 12 EN ðxÞ ¼ Eð0Þ þ 2a ϵ 1  ; ð5Þ xx c N chost 11 is the isolated defect energy. Since the N related where Eð0Þ N hydrostatic deformation potential aN c is not known, we estimate it via [23] aN c ¼ 

host chost 11 þ 2c12 αN ; 3

ð6Þ

containing the pressure coefficient αN of the nitrogen states within the host matrix. For Ga(NAs), the nitrogen level becomes deeper 1 with increasing pressure at a rate of aN [24]. c ¼ 40 meV GPa Additionally, the BAC model introduces the coupling strength V between the resonant defect level and the extended conduction band states [4]. In this work, we use the well established values V ¼ 2:7 eV and EðN0Þ ¼ 1:65 eV [22], which determine the unstrained band gap Egap via [25] " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#  2 1 ð0Þ ð0Þ ð7Þ þ E  Ehost þ4 V 2 xN ; Egap ¼ Ehost gap  E N N 2 gap with the hosts band gap Ehost gap and the impurity concentration xN . All other material parameters required to compute the band structure have been interpolated from their binary constituents taken from Refs. [26,,22]. Finally, we self-consistently solve the Poisson equation [27] to include modifications to the confinement potential of the heterostructure due to local charge distributions.

4. Discussion To get a more pictorial understanding of the system, Fig. 2 (a) summarizes the general structure of the samples together with the most significant wave functions and transitions computed as described in the previous section. Two transitions are of importance in this system. The first ðe3-hh1Þ involves bound states confined to the (GaIn)As layer and is therefore of type-I character

257

Fig. 3. The experimental PL spectra for all samples are shown in frame (a) for an excitation power of 3 Wcm  2 . Frame (b) shows the corresponding theoretically obtained spectra. The calculated transition energies between the relevant states are marked for each sample (also compare Fig. 2(a)). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

while the second ðe1-hh1Þ is a type-II transition across the center GaAs spacing layer with electrons being confined to the Ga (NAs) QW. In Fig. 3(a), we present the PL spectra at 10 K and excitation power 3 Wcm  2 for all three samples which differ in the thickness d of the GaAs spacing layer. For the sample with the thickest spacing layer of d ¼ 5:5 nm (blue line), a single PL peak at 1.251 eV can be observed with a FWHM of 9 meV. It is assigned to the type-I transition e3-hh1 within the (GaIn)As QW. Decreasing the spacing layer thickness to d ¼ 2:5 nm (red line) changes the PL spectrum drastically. The (GaIn)As transition vanishes while at the same time, a new transition occurs at 0:951 eV. With a FWHM of 35 meV, this peak is also considerably broader than the (GaIn)As luminescence. It has been shown that the (GaIn)As/GaAs/Ga(NAs) material system for comparable xIn becomes a type-II semiconductor heterostructure if xN 4 1% [28,29]. The samples under investigation here contain more than 4% N. Accordingly, we ascribe the new peak in the PL spectra to the charge transfer transition e1-hh1 with the electrons confined in the Ga(NAs) QW and the holes in the (GaIn)As region. Further decreasing the spacing layer thickness to d ¼ 0:7 nm leads to an increase in the PL intensity and a slight redshift to 0.935 eV occurs. To strengthen our identification and interpretation of the PL transitions, we conduct rigorous PL calculations according to Section 3 for a density n  n0 ¼ 109 cm  2 . The comparison of both experimental (Fig. 3(a)) and theoretical PL spectra (Fig. 3(b)) shows exceptional agreement. The electronic transition energies are shown as thin vertical lines. Please note that these energies do not coincide with the PL peak positions since they do not contain excitonic binding energies. We can now identify the minor redshift of the PL peak position observed earlier for the sample with d¼ 0.7 nm as a consequence of slightly different material compositions (cf. Table 1). An increasing spatial overlap of the relevant wave functions with decreasing spacing layer thickness results in an enhancement of the dipole matrix element for the indirect transition, ultimately enabling a non-vanishing PL signal. This argument also explains the increase in the type-II PL with decreasing spacing layer thickness. The inhomogeneous broadening for the thick sample is chosen to be Δ ¼ 7 meV while for the indirect type-II PL signals of the other two samples, we used Δ ¼ 35 meV. Since the latter involve states from the N containing layer, the large difference in Δ can be understood as a consequence of N related disorder effects. Electrons confined in the Ga(NAs) can access a broad variety of potential fluctuations and respective electronic states induced by the statically distributed N atoms and related disorder. The recombination with holes in the (GaIn)As QW

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Fig. 4. PL spectra for the sample with d ¼ 2:5 nm for varying pump powers. The PL signal is mainly composed of two different transitions, e1–h1 and e1–h2. The inset shows their evolution with increasing pump power as extracted from the experiment. The solid lines in the inset only act as a guide to the eye. The theoretically predicated PL strengths are depicted as solid (dashed) vertical lines for the h1 (h2) final state.

results in a broad PL band, for which huge FWHM of 35 meV are typical [30,31]. Hence, the calculations confirm our initial interpretation of the nature of the PL. It is interesting to mention that we can resolve an unsettled problem concerning the VBO of Ga(NAs)/GaAs heterostructures on the basis of the discussed exact description of the CT excitons. It has been controversially discussed what type the valence band alignment in Ga(NAs)/GaAs QWs really is. In earlier publications, either a type-I [32,33,7] or a type-II [34,35,8,36–41] band alignment have been proposed. The layout of our structures offers the unique opportunity to study the nature of the valence band offset since the CT-transitions only involve valence band states in the (GaIn)As layer for which the offsets are well known [42]. Therefore, we can determine the Ga(NAs)/GaAs conduction band offset once the BAC parameters are fixed under the premise to reproduce the experimentally observed type-II PL peak position. Since the band gap for Ga(NAs) is experimentally well known and commonly accepted [25,2], we obtain a unique value for the VBO for the Ga(NAs)/GaAs interface. More specifically, we obtain a VBO of 45 meV and a conduction band offset (CBO) of 0.56 eV. These values are with respect to the lh band, which energetically lies above the hh due to shear strain contributions (compare Fig. 2) and are comparable to those from [41]. Although the Stokes shift ΔE is not reproduced in the theoretical PL spectra since our applied microscopic theory does not include disorder effects explicitly, the VBO and CBO values contain it on a phenomenological level. To first order, ΔE scales linearly with the absorption line width Δ according to ΔE ¼ 0:6Δ [43], yielding ΔE ¼ 21 meV. The main source of error regarding our proposed values for the VBO and CBO is the growth-related uncertainty in the material composition and layer thicknesses. We estimate the material composition (layer thickness) to be accurate to 70.5% ð 7 0:5 nmÞ. The resulting uncertainty of the band gap and the confinement energies yield an error of 7 40 meV for the VBO and CBO value. To further analyze the CT-luminescence, we study the normalized PL spectra as a function of excitation power P for the sample with a spacing layer thickness of d ¼ 2:5 nm, depicted in Fig. 4 by the solid lines. For weak excitations up to P ¼ 84 W cm  2 , the CT-PL shifts to higher energies and simultaneously broadens from initially 35 meV to 43 meV, as expected due to Pauli blocking 2 and screening effects. At P ¼ 2 kWcm , the CT-PL changes its shape significantly. The sudden increase of the FWHM up to 108 meV suggests that an additional transition contributes to the line shape. This assumption is emphasized by the decrease of the FWHM at even higher excitation powers. We extracted the energetic positions of both transitions as a function of pump power by fitting two Gaussians to the experimentally observed spectra. The

Fig. 5. Heavy- (black) and light- (red) hole confinement potential for (a) low ðn0 ¼ 1010 cm  2 Þ, (b) medium ð500 n0 Þ, (c) high density ð2000 n0 Þ. Confinement energies for the first (solid), second (dashed), and third (dotted) bound hole states are indicated by horizontal lines. Using the same line types, the corresponding wave functions are shown in frame (d) for a selection of excitation densities. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

results are shown in the inset of Fig. 4. We justify the assignment of specific transitions in the next paragraph. Modifications to the hh and lh band edges and wave functions are of special interest since they can be expected to have more drastic impact on the PL compared to those of the conduction band. Thus, Fig. 5(a)–(c) show the hh (black line) and lh (red line) confinement potentials in real space for different excitation densities. With increasing density, they gradually lose their step-function like appearance and influence the corresponding wave functions. Figure 5(d) shows the valence band wave functions h1, h2, and h3 for the first (solid), second (dashed), and third (dotted) bound hole state, respectively. In contrast to the e1 state (not shown), these wave functions change dramatically with increasing density. Except for the h1 state, the initial carrier localization in the (GaIn)As region changes towards the Ga(NAs) and outer GaAs layer. Besides this relocalization, we observe that the energetic order does not preserve the general shape. Comparing the wave functions for n ¼ 500 n0 (red lines) and n  ncr ¼ 1250 n0 (blue lines), the respective h2 (dashed line) and h3 (dotted line) states have identical shape but switched their energetic order which is a consequence of the band bending shown in Fig. 5(a)–(c). All states are initially confined due to the hh potential. This does not change, even above the critical density ncr , except for the h2 state which is then confined mainly in the Ga(NAs) layer due to the lh potential. Consequently, the overlap between the e1 and h2 wave functions increases significantly, resulting in a stronger dipole matrix element and PL signal, accordingly. 2 2 and 3 kWcm Above the critical density ncr (between 2 kWcm in the experiments), the e1-h2 PL abruptly becomes stronger than the e1-h1 related signal due to two reasons. First, the discussed relocalization of lh confined h2 carriers into the Ga(NAs) layer. Secondly, the occupation of the h2 state increases with enhanced density. The combination of both effects leads to the unusual strong and sudden shift of the main PL peak position observed in the experiment. We show the theoretically predicted PL peak energies for the e1-h1 (h2) transitions along the experimental data in Fig. 4 as solid (dashed)

P. Springer et al. / Journal of Luminescence 175 (2016) 255–259

vertical lines. Furthermore, the height of the vertical bars indicates the relative strength of the transition. It is clearly revealed that the e1-h1 transition defines the PL peak signal for pump powers up to 2 2 2 kWcm . At P ¼ 3 kWcm , the e1-h2 dominates the PL spectrum. Therefore, the conjunction between experiment and theory reveals that the unusual shape of the PL spectra at high excitations densities is a consequence of an interplay between two fundamentally different transitions. Specifically, these are the type-II e1-h1 transition (where electrons are localized in the Ga(NAs) QW and holes in the (GaIn)As layer) and the type-I e1-h2 transition (where holes are shifted to the Ga(NAs) QW).

5. Conclusion We investigated structures designed to show a gradual type-I/ type-II PL crossover by reducing the spacing thickness between a (GaIn)As and a Ga(NAs) QW, and found that the valence band alignment in Ga(NAs)/GaAs QWs possesses weak type-I character. The control of the final heavy-hole state in the (GaIn)As layer eventually allows the determination of the valence band offset of the Ga(NAs)/GaAs interface. This is achieved by tuning this offset to reproduce the experimental PL peak position for the transition across the spacing layer. We were able to quantify the VBO of (45 7 40 meV) with a resulting CBO of ð0:56 7 0:04Þ eV. Our statement is sustained by the excellent agreement between experiment and calculations based on the semiconductor luminescence equations. A study of the pump power dependency reveals that different transitions dominate the PL spectrum at different excitation conditions. With increasing density, the valence band morphs due to local charge inhomogeneities. While the first heavy-hole state remains in the (GaIn)As layer, the second gets redistributed from there into the Ga(NAs) QW. This redistribution of holes in turn increases the overlap to the involved conduction band wave function, which strengthens the PL signal related to that transition. The interplay between these transitions is responsible for the experimentally observed unusually broad line shape of the PL spectrum.

Acknowledgments We gratefully acknowledge financial support by the DFG in the framework of the SFB 1083 and GRK 1782. The work of J.H. and J.V. M. is supported by the US AFOSR via Contract FA9550-14-1-0062.

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