Theoretical luminescence spectra in p-type superlattices based on InGaAsN
© de Oliveira et al.; licensee Springer. 2012
Received: 9 July 2012
Accepted: 19 October 2012
Published: 31 October 2012
In this work, we present a theoretical photoluminescence (PL) for p-doped GaAs/InGaAsN nanostructures arrays. We apply a self-consistent method in the framework of the effective mass theory. Solving a full 8 × 8 Kane's Hamiltonian, generalized to treat different materials in conjunction with the Poisson equation, we calculate the optical properties of these systems. The trends in the calculated PL spectra, due to many-body effects within the quasi-two-dimensional hole gas, are analyzed as a function of the acceptor doping concentration and the well width. Effects of temperature in the PL spectra are also investigated. This is the first attempt to show theoretical luminescence spectra for GaAs/InGaAsN nanostructures and can be used as a guide for the design of nanostructured devices such as optoelectronic devices, solar cells, and others.
KeywordsDilute nitride semiconductor Luminescence method p-doped Nanostructures
In the last decade, the study of quaternary InGaAsN alloy systems has attracted a great deal of attention due to its potential application in nanostructured devices such as next-generation multijunction solar cells and optoelectronic devices for optical communications [1–5]. Incorporation of a small amount of nitrogen (<2%) to InGaAs reduces the net strain because of the smaller atomic size of nitrogen (0.75 Å) compared with arsenic (1.33 Å), decreasing the bandgap due to a large bandgap bowing . Therefore, by carefully controlling the composition ratios, one should be able to achieve InGaAsN epitaxial layers lattice-matched to GaAs substrates . The use of these alloys in the manufacture of laser regions for optical communication emitting at the range of 1.3 to 1.5 μm shows several advantages, e.g., it has been demonstrated to be a low-cost replacement for directly modulated 1.3-μm InP devices used in network applications as wireless access points and Ethernet switches [8, 9]. In addition, the diluted quaternary nitride alloys are of great interest for high-conversion efficiency solar cells and heterojunction bipolar transistors (HBT) with low turn-on voltage for portable devices [2–5]. For space photovoltaic applications, high-efficiency solar cell are advantageous for increasing the available electrical power or alternately reducing satellite mass and launch cost .
In order to improve the development of new dilute nitride-based devices, it is important to investigate the photoluminescence (PL) properties of semiconductor nanostructures . Although an investigation on the PL properties of p-type-doped InGaAsN systems is of particular interest due to its potential usage in n-p-n HBT devices as the base layer [11–15], few reports are found on the literature. Generally, beryllium has been used as the p-type dopant in the InGaAsN layers [10, 11]. From an experimental point of view, rapid thermal annealing (RTA) has been demonstrated to improve the PL intensity and the internal quantum efficiency of solar cells . The real importance of this technique is that RTA can effectively reduce the composition fluctuation and suppress the InGaAs-rich phase . This fact was also observed in GaAsN alloys, confirming the formation of localized states inside the wells .
In this work, we investigate the theoretical PL spectra calculations for p-doped GaAs/InGaAsN nanostructures. The calculations are performed within the method by solving the full 8 × 8 Kane's Hamiltonian, generalized to treat different materials. Strain effects due to the lattice mismatch between InGaAsN and GaAs are also taken into account. By varying the acceptor concentration and well width, we analyze the effect of exchange-correlation, which plays an important role in the potential profile and electronic transitions. We also investigate the effects of temperature in the PL spectra. These results can explain several important aspects on the optical properties of these nanostructured systems.
The calculations are carried out by solving the 8 × 8 Kane's multiband effective mass equation (EME) which is represented with respect to a basis set of plane waves. We assume an infinite superlattice (SL) of squared well along the <001 > direction. The multiband EME is represented with respect to the plane waves with the wave vectors, K = (2π/d)l (l is an integer), equal to the reciprocal SL vectors. Rows and columns of the 8 × 8 Kane's Hamiltonian refer to the Bloch-type eigenfunctions of the Γ8 heavy and light hole bands, Γ7 spin-orbit hole bands, and Γ6 electron bands; denotes a vector of the first Brillouin zone.
where p x is the dipole momentum in the direction x; σ e and σ q denote the spin values for electrons and holes, respectively. We consider the gap energy for InGaAsN alloys as described in . We also used an approach for different temperatures, considering the Varshni correction as given in . However, it is important to note that for the reported high concentrations of In (0.25 to 0.41) and N (0 to 0.052) at low temperatures (T < 60 K), the PL spectra shows an energy blueshift, mainly due to the recombination of excitons localized most likely in the In-N clusters .
Results and discussion
We present here for the first time the theoretical PL spectra for GaAs/InGaAsN systems obtained using self-consistent effective mass theory calculations. We noted a remarkable change in the total potential when the acceptor concentration increases. For the cases discussed here, changes in the well width do not change the shape of bending for the total potential. Furthermore, and as expected, we see a redshift in the PL spectra as the temperature increases. The present results show that in modulation p-doped GaAs/InGaAsN nanostructures, the many-body effects, such as exchange and correlation, must be taken into account for a realistic description of hole bands and potentials in these systems. These findings will certain have important implications for optical measurements, such as luminescence or absorption, towards developing new technologies based on nanostructured superlattices. This will be important in the development of new optoelectronic devices, solar cells, and other devices.
The authors thank the support received from the Brazilian research financial agencies CNPq (grants no. 564.739/2010-3/NanoSemiCon, 302.550/2011-9/PQ, 470.998/2010-5/Univ, 472.312/2009-0/PQ, 303578/2007-6/PQ, and 577.219/2008-1/JP), CAPES, FACEPE (grant no. 0553–1.05/10/APQ), and FAPESP. Luísa MR Scolfaro also acknowledges partial support from the Materials Science, Engineering and Commercialization Program of Texas State University.
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