Optical Investigation of p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs Quantum Wells Emitters

We have studied the 1.55 μ m optical properties of p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum wells using a self-consistent calculation combined with the anticrossing model. We have found that the increase of injected carriers’ density induces the increase of optical gain and radiative current density. The rise of doping density causes a blue shift of the fundamental transition energy accompanied with signiﬁcant increase of optical gain. The quantum-conﬁned Stark eﬀect on radiative current density is also studied. The variation of radiative current as function of well width and Sb composition is also examined. In order to operate the emission wavelength at the optical ﬁber telecommunication domain, we have adjusted the well parameters of p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs.


Introduction
Antimony-based III-V semiconductors have a great interest in the field of optoelectronics for the design of long wavelength infrared detection devices [1][2][3]. In fact, these compounds reveal motivated electrical and optical properties, especially a significant reduction of the gap covering the telecom and the long infrared domains [4,5]. Technological progress in growth techniques, such as molecular beam epitaxy (MBE) and metal organic chemical vapor deposition, offers the opportunity to control the incorporation of small Sb or N amounts into GaAs host matrix. In fact, the incorporated N atom induces a strong band gap reduction around 180 meV/%N [6][7][8][9][10]. As proof of this behavior, Chakir et al. [7] have studied the band structure reconstruction of GaAs 1-x N x using the 10 × 10 band anticrossing (BAC) model. Similarly, the incorporation of Sb leads to a band gap reduction of about 16 meV/%Sb [11,12]. Alberi et al. [11] have used the 12 × 12 BAC model to calculate the valence bands in GaAs 1-x Sb x material. Consequently, the simultaneous incorporation of N and Sb into GaAs matrix accelerates the ratio of the band gap reduction. Experimental reported works [12][13][14][15] indicate that the band gap of GaAs 0.89 N 0.03 Sb 0.09 material reaches a low value of 0.835 eV. Also, many research groups have succeeded in developing thin film structures based on GaAs1-x-yNxSby for telecommunication in the optical windows 1.3 and 1.55 μm characterized by high transmission. Indeed, Harmand et al. [16,17] reported the elaboration of high crystalline GaNx As 1-x-y Sb y /GaAs structures with wavelength emission 1.3-1.55 μm.
ey stated the improvement of photoluminescence property after thermal annealing. Lin et al. [18] and Lourenço et al. [19] [21]. Tan et al. [22] examined the optical absorption of the p-i-n GaNAsSb/GaAs structure emitting at 1.3 µm. ey found that the absorption coefficient is about 1.3 10 4 cm −1 . Luo et al. [23] reported that the absorption coefficient of GaNAsSb/GaAs double-QWs emitting at 1.55 μm is equal to 2 10 4 cm −1 . e purpose of this work is to investigate the optical gain and radiative current density of 1.55 µm p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum wells emitters. We examined the dependence of optical gain on the injected carrier density and doping effect. In addition, the applied electric field, well width, and Sb composition effects on the radiative current density are also discussed.

Theory
In this part, we detail a theoretical model used to calculate the electronic and optical properties of p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum wells. For this particular structure, it should be noted that the x composition of nitrogen is chosen as x � 0.38y that ensures zero mismatch between GaNAsSb alloy and GaAs substrate. In fact, we have used the (16 × 16) BAC model combined with self-consistent calculation. e Schrödinger equation is solved taking into account the band discontinuity between the GaAs barrier and GaNAsSb well ∆U. e Hartree potential U H (z) and the exchange-correlation potential U xc (z) are obtained by solving Poisson's equation. e term eFz is linked to the Stark effect [24,25]: where m * e,h is the effective masses of electrons or holes, E k and φ k are, respectively, the k th energy level and the envelope wavefunction, φ k (z) satisfies the boundary condition at the interface z 0 � 0 and z 0 � L w , N d (z) and N a (z) are, respectively, the ionized donor and acceptor doping concentrations, and n(z) and p(z) are the carrier densities of electrons and holes, respectively. e optical performances for p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs QW laser structures are estimated in terms of optical gain and radiative current density. e optical gain calculated at photon energy E is obtained with the contribution of the fundamental transitions T ei−hi for k p � 0. It was described by the following expression [26,27]: where C and ε 0 are, respectively, the velocity of light and permittivity of free space, n and L w are the refractive index and well width, respectively, I e i h i is the wave function envelope, ρ j i2D is the two-dimensional density state, |M j i (E p )| 2 is the optical transition matrix element between heavy hole subband h i and electron subband e i for TE polarization, L j i (E, E p ) is the Lorentzian line shape function, and f n c (E p ) and f m v (E p ) are, respectively, Fermi functions for the n th subband in the conduction band and m th subband in the valence band [28].
For an ideal laser without any nonradiative recombination processes, the radiative current density is given by the following formula [29]: where B and N i are, respectively, the spontaneous radiative recombination coefficient and the injected carrier density [30].
where e is the electron charge, E g is the band gap energy, m 0 is the free electron mass, |M avr | 2 is the average of the squared of the momentum matrix element, k b is the Boltzmann constant, and r � (m * e /m * h ) is the ratio of the electron and hole effective masses [31].

Results and Discussion
e electronic band structure of p-GaAs/i-GaN 0.070 As 0.743 Sb 0.186 /n-GaAs QW without and under an applied electric field F � 40kV/cm is shown in Figure 1. e donor and acceptor doping concentrations are equal to 2 × 10 18 cm −3 and 3 × 10 18 cm −3 , respectively. All calculations were performed with temperature 300 K as the input parameter. e Sb composition and well thickness are equal to y Sb � 18.6% and L w � 4 nm, respectively. Figure 2 shows the variation of maximum gain G max and radiative current density J rad as function of the injected carrier density N i for p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum well structures. e optimized well parameters give rise to λ e 1 −h 1 � 1.55 μm. By increasing the injected carrier 2 Journal of Nanotechnology density from 5 × 10 17 to 2 × 10 18 cm −3 , the optical gain increases from 8.65 × 10 3 to 6 × 10 4 cm −3 . Likewise, the radiative current density magnitude rises from 14.41 to 133.7 A/ cm 2 . e same behavior was observed by Liu et al. [32]. ey indicated an enhancement in optical gain varying the carrier concentrations from 8 × 10 18 to 2.4 × 10 19 cm −3 for GaAsSb/ GaAs quantum well lasers. Furthermore, Park et al. [33] studied the optical gain as functions of carrier density and the radiative current density for the GaAsSbN/GaAs QW structures emitting at 1.3 µm wavelength. ey showed that optical gain in GaAsSbN/GaAs QW structures is about 2.8 × 10 3 cm −3 , which is higher than GaAsSb/GaAs QW. ey also illustrated that the radiative current density of GaAsSbN/GaAs is nearly the same as that of the InGaAsN/ GaAs QW structure. In another study, Park et al. [34] reported the dependence of the optical gain on the carrier density for GaAsSbN/GaAs QW structures with several compressive strains. Chen et al. [35] studied the dependence of gain maximum of W structure with 3 nm compressively strained GaAs 0.35 Sb 0.65 layers for three different carriers' concentrations. For 3 nm InGaAs/3 nm GaAsSbBi QW [36], TE material gain increases when the carrier concentration varies from 2 × 10 18 to 6 × 10 18 cm −3 . e calculated optical gain for doped GaNAsSb well for p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum well laser is shown in Figure 3. It was significantly enhanced from 4 × 10 3 to 9.6 × 10 3 cm −3 with increasing doping density from 5 × 10 16 to 1.5 × 10 17 cm −3 . Similarly, Kim et al. [21] reported the increase of optical gain as function of doping densities of the GaSb 0.24 As 0.76 /In 0.26 Ga 0.74 N 0.06 As 0.94 /GaAs QW structure. ey claim that this behavior can be explained by the fact that the optical matrix element increases with increasing doping density. Jiang et al. [37] examined the gain spectra for TE-polarized light, the n-doped Ge/GeSi quantum well under various n-type doping concentrations. ey indicated that at low strain level, the optical gain could be enhanced when n-type doping concentration increases from 5 × 10 18 to 5 × 10 19 cm −3 . On the other hand, Huang et al. [38] studied the variation of maximum gain of Ge 0.9375-m Sn 0.0625 P m , Ge 0 . 9375-m Sn 0 . 0625 As m , Ge 0.9375-m Sn 0 . 0625 Sb m , and Ge 0 . 9375-m Sn 0 . 0625 Bi m as a function of doping concentration for an injected carrier density of 1 × 10 19 cm −3 . ey illustrated that the gain increase as function of the doping concentration, and the effects of the doping elements on the optical gain of GeSn can be ranked as Bi > Sb > As > P.
We investigated the effect of the applied electric field on the radiative current density for p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs QW structure operating at 1.55 µm telecommunication wavelength, as shown in Figure 4. e antimony composition and well thickness are y Sb � 18.6% and L w � 4.1 nm, respectively. e calculated radiative current increases from 67.07 to 102.64 A/cm 2 when F changes from 0 up to 40 kV/cm. is behavior was stated in our previous work [39] for p-GaAs/i-GaNAsBi/n-GaAs QWs. We mentioned that the radiative current density varies from 101.3 to 515.3 A/cm 2 , with increasing the electric field from 0 up to 40 kV/cm. e rise of the current density is also indicated by Mensfoort et al. [40] for blue polymerbased light-emitting diodes. ey interpret this increase by the improvement of the net space charge density caused by the reduced recombination rate for small voltages. e radiative current density J rad as well as the fundamental transition energy as function of well width L w is shown in Figure 5(a). J rad increases from 37.81 to 151.04 A/ cm 2 . e increase of L w from 4 to 4.5 nm induces a significant red-shift of fundamental transition energy from 802 to 774 meV. In another study, Bilel et al. [41] stated that the shift of the fundamental transition energy T e1-h1 to lower energies can be explained by the modification of the electron and hole subbands under the effect of the applied electric field. To correct this shift, we adjusted the Sb composition y Sb for each used value of well width L w . e optimized values of y Sb are, respectively, equal to 17.8 and 18.8% for 4 and 4.5 nm, as shown in Figure 5(b). e radiative current density varies 47 from to 144.7 A/cm 2 at 1.55 μm telecommunication wavelength.     : e radiative current density as function of applied electric field F varying from 0 up to 40 kV/cm for p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs QW structure operating at 1.55 μm telecommunication wavelength. e Sb composition and the well width are y Sb � 18.6% and L w � 4.1 nm, respectively. Such optimization of the well parameters (well thickness and Sb composition) seems to be interesting investigation to enhance the optoelectronic performance of 1.55 μm p-GaAs/ i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum wells emitters.

Conclusion
e optoelectronic properties of 1.55 μm p-GaAs/i-GaN 0.38y As 1-1.38y Sb y /n-GaAs quantum wells were theoretically investigated using a self-consistent calculation combined with an anticrossing model. e maximum of gain is enhanced with increasing the injected carrier density. e optical gain reaches the value 9.6 × 10 3 cm −1 for doping density equal to 1.5 × 10 17 cm −3 . Moreover, the applied electric field significantly affects the radiative current density of the studied structure. e radiative current density is about 151.04 A/cm 2 for 4.5 nm well width. e fundamental transition energy T e1-h1 shifts from 28 meV to lower energies when the well width varies from 4 to 4.5 nm. We can conclude that the obtained results are advantageous to the design of p-i-n based GaNAsSb quantum well laser structures operating at 1.55 µm telecommunication wavelength.

Data Availability
e datasets used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest.