Open Access
Add to BibSonomyAbstract
An investigation of the effects of an embedded AlGaN δ-layer on the photoluminescence (PL) efficiency of an InGaN/GaN single quantum well (SQW) is presented. In particular, we focus on the dependence of the overlap integral between the electron and hole envelope wavefunctions on the AlGaN δ-layer thickness, aluminum composition, and Mg δ-doping concentration. We have demonstrated by means of simulation and experiment that the overlap integral and PL efficiency are enhanced with increasing δ-layer thickness. They have been shown to be raised further by increasing aluminum composition and Mg δ-doping concentration in the δ-layer.
©2007 Optical Society of America
1. Introduction
The III-V nitride semiconductors such as GaN, AlN, InN, and their alloys have been successfully used for light emission ranging from deep UV to infrared [1]. For long-wavelength emission, however, we still have difficulty in designing c-oriented InGaN/GaN quantum wells (QWs) due to the presence of the piezoelectric polarization along with the spontaneous polarization induced by large lattice mismatch [2]. A general approach to controlling long-wavelength tuning, especially for green light emission, is to increase the InGaN QW thickness and/or the indium content. Increasing the QW thickness, however, brings in the strong piezoelectric field effects, lowering substantially the optical transition probability [2]; on the other hand, increasing the indium content introduces several defects such as V-defects, stacking faults, and dislocations [3], thereby inducing numerous non-radiative recombination centers. For these reasons, one more green light-emitting diode (LED) is inevitably deployed in a LED array light module for white backlight (i.e., RGB array: one blue + one red + two green LEDs) for LCD flat panel displays [4]. In addition, a green laser that is highly demanded for full-color projectors has very high threshold current density [5].
As part of an effort to bypass the piezoelectric field effects, many researchers are lately interested in the growth of InGaN/GaN QWs on nonpolar planes (m-plane {101¯0} or a-plane {112¯0} [6]) or semipolar {112¯2} GaN substrates [7]. However, the crystal quality grown in the nonpolar directions is still much poorer and the external quantum efficiency of a LED based on the semipolar GaN substrates is very low [7]. What is worse, those semipolar or nonpolar substrates are highly priced. Recently, a novel QW structure based on a c-oriented thick InGaN single quantum well (SQW) with an embedded AlGaN δ-layer has been proposed in [8]. It has been demonstrated theoretically and experimentally that the δ-layer offers an extra degree of freedom in tuning the emission wavelength and most importantly, long-wavelength tuning is feasible with lower indium composition. Furthermore, the δ-layer is shown to shorten the photoluminescence (PL) lifetime. In this paper, with attempt to gain more insight into the δ-layer effects in the existence of spontaneous and piezoelectric polarizations, we make an in-depth investigation of the effects of the δ-layer thickness, aluminum composition, and Mg-doping level on the overlap integral between the electron and hole envelope wavefunctions.
2. Theory and experiment
To make a theoretical study, we have solved 1D Poisson’s equation [9] that incorporates the built-in sheet charge due to spontaneous and piezoelectric polarizations, which is written as;
where the variable ψ represents the electrostatic potential, n and p the electron and hole densities, respectively, ND and NA the donor and acceptor impurity concentrations, respectively, and Psp(x) the spontaneous polarization. The last term describes the piezoelectric polarization. The variable x indicates the In mole fraction. All the other parameters are the same as defined in Ref. [9]. In addition, we have solved the effective-mass Schrödinger equation [10] for quantum energy levels and associated envelope wavefunctions. Poisson’s equation is solved by Newton-Raphson iteration and the effective-mass Schrödinger equation by the inverse power method, all of them on a finite difference approximation. In the model, the strain effects of those wurtzite semiconductor materials are considered and the phenomena such as the tilt of the energy band and the spatial separation of electrons and holes are all captured. The band-offset ratio (ΔEc/ΔEv) of InGaN/GaN and AlGaN/GaN is assumed to be 0.7/0.3 [11] and 0.67/0.33 [12], respectively.
To confirm the soundness of our numerical calculation, we have grown InGaN/GaN QW layers on (0001) sapphire substrates by metal-organic vapor phase epitaxy (MOVPE) and performed PL measurements at room temperature using a frequency-doubled Ti:sapphire laser at 400nm wavelength. The QW structure consists of an Al0.05Ga0.95N δ-layer embedded in the center of a thick undoped In0.15Ga0.85N SQW sandwiched between 6.2-nm-thick GaN barriers. The indium composition and total QW thickness (excluding the δ-layer thickness) are measured to be 15% and 4nm, respectively, by the x-ray rocking curve analysis. The AlGaN δ-layer was grown at the same growth temperature as the InGaN SQW. Low (740°C) and high (1320°C) temperature deposited GaN buffer layers were used to improve the quality of upper-grown barriers and QWs.
3. Results and discussion
Fig. 1. Energy band diagrams and wavefunctions of (a) 4-nm-thick In0.15Ga0.85N SQW (Tδ=0nm), (b) QW with Tδ of 0.4nm, i.e., In0.15Ga0.85N (2nm) - Al0.05Ga0.95N (0.4nm) -In0.15Ga0.85N (2nm) QW, and (c) QW with Tδ of 1.0nm sandwiched between 10-nm-thick GaN barriers, calculated with no built-in interface polarization charge considered.
Fig. 2. Overlap integral between the electron and hole envelope wavefunctions as a function of the δ-layer thickness obtained without built-in interface polarization charge.
We first investigate the effects of the δ-layer thickness on the overlap integral between the electron and hole envelope wavefunctions when built-in interface polarization charge in Eq. (1) is neglected. Displayed in Fig. 1 are the energy band diagrams and lowest subband wavefunctions for different δ-layer thicknesses (Tδ). For a comparison, we have also calculated those of the same-thick (4nm) InGaN SQW (i.e., Tδ=0nm) as depicted in Fig. 1(a). The overlap integral values quantified from the results in Fig. 1 are presented in Fig. 2. It is clearly seen that as Tδ increases, the overlap integral is rather decreased. If no polarization charge is involved, therefore, there is no need to use a δ-layer for enhancing the PL efficiency of InGaN/GaN QWs. In reality, however, the strong built-in polarization field that is parasitic on GaN wurtzite semiconductors reduces dramatically the oscillator strength [2], resulting in a decrease of the internal quantum efficiency.
Shown in Fig. 3 are the energy band diagrams and lowest subband wavefunctions when built-in interface polarization charge in Eq. (1) is considered. It is evident that most of electrons and holes are localized separately when the δ-layer is zero thick as seen in Fig. 3(a). As Tδ increases, the electron wavefunction is further expanded toward the n-side (the right-hand side of the diagram) and the hole wavefunction to the p-side of the QW as shown in Figs. 3(b) and 3(c), possibly enhancing the overlap integral between them, to which the optical matrix element is proportional [10]. It is likely that comparing to the electron wavefunction, the hole wavefunction is less sensitive to the δ-layer thickness, due mainly to its large effective mass.
Fig. 3. Energy band diagrams and wavefunctions of (a) 4-nm-thick In0.15Ga0.85N SQW, (b) QW with Tδ of 0.4nm, and (c) QW with Tδ of 1.0nm sandwiched between 10-nm-thick GaN barriers, obtained with built-in interface polarization charge considered.
We have quantified the overlap integral from the results in Fig. 3 as a function of T δ for different In mole fractions of the QWs and presented the results in Fig. 4. For a comparative study, we have also presented the simulation results of the same-thick (4nm) and half-thick (2nm) SQWs. Unlike the conclusion drawn from the results in Figs. 1 and 2, the overlap integral is found to be raised with increasing δ-layer thickness in the presence of built-in polarization charges. To support our numerical prediction, we have measured the PL peak intensities of the grown QW samples for the indium content in the QW as high as 15%. Because the optical matrix element is proportional to the overlap integral, indeed the PL intensity is measured to be enhanced with increased δ-layer thickness as evident in Fig. 4. It is noted that care was taken to ensure that all the samples were measured under the same condition in order to be able to compare the emitted intensities. For the reason, it appears to be desirable to use a thicker δ-layer for higher PL efficiency. However, one also needs to consider the emission wavelength (transition energy), which also depends sensitively on the δ-layer thickness [8], providing an extra degree of freedom in the wavelength-tuning control. In other words, in the case where longer-emission wavelength is desired, for example, green-emission wavelength, there exists a tradeoff between the PL efficiency and the PL transition energy on the selection of the d-layer thickness. In Ref. [8], it has been demonstrated that the PL peak wavelength of thick SQWs with a δ-layer always lies between or rather bounded by those of the half-thick (2nm) and the same-thick (4nm) SQWs, a similar behavior also observed in the PL intensity as seen in Fig. 4. For a given T δ, we can confirm that the overlap integral is getting reduced with increased indium content since the tilt of the energy band is steeper.
Fig. 4. Overlap integral as a function of the δ-layer thickness obtained with built-in interface polarization charge considered for different indium compositions. The PL peak intensity has been measured for the indium composition of 15%.
Fig. 5. Measured PL intensity at room temperature versus the δ-layer thickness for different laser pump powers (densities) (PL) when the indium composition is as high as 15%.
We have further measured the PL intensity of the grown QW samples with 0.4-nm, 0.8-nm, and 1.2-nm-thick AlGaN δ-layers for different laser pump powers (densities) at room temperature and presented the results in Fig. 5. As expected, the PL intensity is raised with increasing δ-layer thickness at any laser pump power (density). The numerical prediction is therefore in qualitatively good agreement with the experimental results. With the validated numerical model, we carry out a numerical investigation of the PL dependence on the aluminum composition and Mg δ-doping concentration below.
It is well known that a barrier height is of importance in the design of QW structures. Likewise, the δ-layer height (i.e., the bandgap energy of an AlGaN material varying depending on the aluminum content) may affect the PL efficiency of InGaN/GaN QWs. As such, an investigation of the effects of the δ-layer height on the overlap integral deserves to be made. Shown in Fig. 6 is the overlap integral with respect to the δ-layer thickness for different aluminum compositions. The overlap integral is observed to be raised with increasing aluminum content. This could be ascribed to the fact that more electrons and holes are confined in the right- and left-hand sides of the QWs in Fig. 3, respectively, when the δ-layer height is increased, thereby increasing the electron-hole wavefunction overlap.
Fig. 6. Overlap integral versus the δ-layer thickness for different aluminum compositions of the δ-layer when the indium content in the QW is as high as 15%.
Fig. 7. Overlap integral as a function of Mg-doping concentrations in the δ-layer for different indium contents when the δ-layer thickness is 0.4nm.
Finally, we inquire into the effects of Mg doping into the AlGaN δ-layer on the overlap integral. A lot of efforts have been made to achieve p-type AlGaN with Mg. High carrier concentration (>3×1018cm-3) has been obtained using Mg-doped AlGaN/GaN strained layer superlattices [13]. Furthermore, Mg-delta doping into GaN [14] has been shown to significantly increase the hole concentration. Therefore, an investigation of the δ-doping effects on the overlap integral deserves to be made. Figure 7 shows the overlap integral calculated as a function of Mg-doping levels in the d-layer for different indium contents in the QW when the δ-layer thickness is 0.4nm. It is found that the overlap integral is enhanced as the Mg-doping concentration increases, a phenomenon originating most likely from the screening effect by free carriers in the δ-layer.
4. Conclusion
We have demonstrated that the overlap integral (or rather the PL efficiency of InGaN SQW) between the electron and hole envelope wavefunctions can be enhanced by adjusting the embedded AlGaN δ-layer thickness, aluminum composition, and δ-doping concentration. It has been addressed theoretically and experimentally that the PL efficiency is enhanced with increasing δ-layer thickness. It can be further raised by increasing the aluminum content (i.e., δ-layer height) and/or Mg-doping concentration in the δ-layer.
References and links
1. D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8, 310–320 (2002). [CrossRef]
2. J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlxGa1-xN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998). [CrossRef]
3. M- Shiojiri, C. C. Chuo, J. T. Hsu, J. R. Yang, and H. Saijo, “Structure and formation mechanism of V defects in multiple InGaN/GaN quantum well layers,” J. Appl. Phys. 99, 073505–1–073505–6 (2006).
4. R. S. West, H. Konijn, S. Kuppens, N. Pfeffer, Q. V. V. Vader, Y. Martynov, T. Heemstra, and J. Sanders, “LED backlight for large area LCD TV’s,” http://www.lumileds.com.
5. S.-I. Nagahama, M. Sano, T. Yanamoto, D. Morita, O. Miki, K. Sakamoto, M. Yamamoto, Y. Matsuyama, Y. Kawata, T. Murayama, and T. Mukai, “GaN-based laser diodes emitting from ultraviolet to blue-green,” Proc. SPIE 4995, 108–116 (2003). [CrossRef]
6. A. Chitnis, C. Chen, V. Adivarahan, M. Shatalov, E. Kuokstis, V. Mandavilli, J. Yang, and M. A. Khan, “Visible light-emitting diodes using a-plane GaN-InGaN multiple quantum wells over r-plane sapphire,” Appl. Phys. Lett. 84, 3663–3665 (2004). [CrossRef]
7. M. Funato, M. Ueda, Y. Kawakami, Y. Narukawa, T. Kosugi, M. Takahashi, and T. Mukai, “Blue, Green, and Amber InGaN/GaN Light-Emitting Diodes on Semipolar {112¯2} GaN Bulk Substrates,” Jpn. J. Appl. Phys. 45, L659–L662 (2006). [CrossRef]
8. J.-W. Park and Y. Kawakami, “Photoluminescence Property of InGaN single quantum well with Embedded AlGaN δ-layer,” Appl. Phys. Lett. 88, 202107–1–3 (2006).
9. O. Mayrock, H.-J. Wünsche, and F. Henneberger, “Polarization charge screening and indium surface segregation in (In,Ga)N/GaN single and multiple quantum wells,” Phys. Rev. B 62, 16870–16880 (2000). [CrossRef]
10. S. L. Chuang and C. S. Chang, “k∙p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996). [CrossRef]
11. C. G. Van de Walle and J. Neugebauer, “Small valence-band offsets at GaN/InGaN heterojunctions,” Appl. Phys. Lett. 70, 2577–2579 (1997). [CrossRef]
12. J. Piprek, R. K. Sink, M. A. Hansen, J. E. Bowers, and S. P. Denbaars, “Simulation and Optimization of 420nm InGaN/GaN Laser Diodes,” Proc. SPIE 3944–03, 28–39 (2000). [CrossRef]
13. J. K. Sheu, G. C. Chi, and M. J. Jou, “Low-operation voltage of InGaN/GaN light-emitting diodes by using a Mg-doped Al0.15Ga0.85N/GaN superlattice,” IEEE Elec. Dev. Lett. 22, 160–162 (2001). [CrossRef]
14. Y.-B. Pan, Z.-J. Yang, Y. Lu, M. Lu, C.-Y. Hu, T.-J. Yu, X.-D. Hu, and G.-Y. Zhang, “Improvement of properties of p-GaN by Mg delta doping,” Chin. Phys. Lett. 21, 2016–2018 (2004). [CrossRef]
