# Optical Investigation of p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs Quantum Wells Emitters

Authors: I. Guizani; C. Bilel; Malak Alrowaili; A. Rebey
Journal: Journal of Nanotechnology
 (2022)

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## Abstract

We have studied the 1.55μm optical properties of p-GaAs/i-GaN0.38yAs1-1.38ySby/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-GaN0.38yAs1-1.38ySby/n-GaAs.


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## Body

## 1. Introduction

Antimony-based III-V semiconductors have a great interest in the field of optoelectronics for the design of long wavelength infrared detection devices [1–3]. 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 [6–10]. As proof of this behavior, Chakir et al. [7] have studied the band structure reconstruction of GaAs1-xNx 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 GaAs1-xSbx material. Consequently, the simultaneous incorporation of N and Sb into GaAs matrix accelerates the ratio of the band gap reduction. Experimental reported works [12–15] indicate that the band gap of GaAs0.89N0.03Sb0.09 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 GaNxAs1-x-ySby/GaAs structures with wavelength emission 1.3–1.55 μm. They stated the improvement of photoluminescence property after thermal annealing. Lin et al. [18] and Lourenço et al. [19] elaborated 1.3 μm (i.e., 0.95 eV) GaNxAs1-x-ySby/GaAs structures. The energy band diagram of GaAsSbN has been computed by using the double BAC model consisting of a conduction BAC model and a valence BAC model. More advanced, Ohtani et al. [20] elaborated n-doped InAs/AlSb quantum structures using MBE. The doping effect on the optoelectronic properties of type II GaAs.76Sb.24/In.26Ga.74N.06As.94/GaAs QW was studied by Kim and Park [21]. Tan et al. [22] examined the optical absorption of the p-i-n GaNAsSb/GaAs structure emitting at 1.3 µm. They found that the absorption coefficient is about 1.3 104 cm−1. Luo et al. [23] reported that the absorption coefficient of GaNAsSb/GaAs double-QWs emitting at 1.55 μm is equal to 2 104 cm−1.The purpose of this work is to investigate the optical gain and radiative current density of 1.55µm p-GaAs/i-GaN0.38yAs1-1.38ySby/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.


## 2. Theory

In this part, we detail a theoretical model used to calculate the electronic and optical properties of p-GaAs/i-GaN0.38yAs1-1.38ySby/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. The Schrödinger equation is solved taking into account the band discontinuity between the GaAs barrier and GaNAsSb well ∆U. The Hartree potential UHz and the exchange-correlation potential Uxcz are obtained by solving Poisson’s equation. The term eFz is linked to the Stark effect [24, 25]:(1)−ℏ22me,h∗∇2+ΔUz+UHz+Uxcz+eFzφkz=Ekφkz,d2UHzdz2=e2ε0εrpz−Naz+Ndz−nz,where me,h∗ is the effective masses of electrons or holes, Ek and φk are, respectively, the kth energy level and the envelope wavefunction, φkz satisfies the boundary condition at the interface z0=0 and z0=Lw, Ndz and Naz are, respectively, the ionized donor and acceptor doping concentrations, and nz and pz are the carrier densities of electrons and holes, respectively.The optical performances for p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs QW laser structures are estimated in terms of optical gain and radiative current density. The optical gain calculated at photon energy E is obtained with the contribution of the fundamental transitions Tei−hi for kp=0. It was described by the following expression [26, 27]:(2)GE,Ep=1Lwe2ℏm02nε0Ec∑i,jIhiei∫0∞ρi2DjMijEp2fcnEp−fvmEpLijE,EpdEp,where C and ε0 are, respectively, the velocity of light and permittivity of free space, n and Lw are the refractive index and well width, respectively, Ihiei is the wave function envelope, ρi2Dj is the two-dimensional density state, MijEp2 is the optical transition matrix element between heavy hole subband hi and electron subband ei for TE polarization, LijE,Ep is the Lorentzian line shape function, and fcnEp and fvmEp are, respectively, Fermi functions for the nth subband in the conduction band and mth 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]:(3)Jrad=eLwBNi2,where B and Ni are, respectively, the spontaneous radiative recombination coefficient and the injected carrier density [30].(4)B=e2LwnEgMavr2m02ε0c3kbTmh∗1+r,where e is the electron charge, Eg is the band gap energy, m0 is the free electron mass, Mavr2 is the average of the squared of the momentum matrix element, kb is the Boltzmann constant, and r=me∗/mh∗ is the ratio of the electron and hole effective masses [31].


## 3. Results and Discussion

The electronic band structure of p-GaAs/i-GaN0.070As0.743Sb0.186/n-GaAs QW without and under an applied electric field F=40kV/cm is shown in Figure 1. The donor and acceptor doping concentrations are equal to 2 × 1018 cm−3 and 3 × 1018 cm−3, respectively. All calculations were performed with temperature 300 K as the input parameter. The Sb composition and well thickness are equal to ySb=18.6% and Lw=4nm, respectively.Figure 1
Band diagram of p-GaAs/i-GaN0.070As0.743Sb0.186/n-GaAs QW without and under an applied electric field F = 40 kV/cm.Figure2 shows the variation of maximum gain Gmax and radiative current density Jrad as function of the injected carrier density Ni for p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs quantum well structures. The optimized well parameters give rise to λe1−h1=1.55μm. By increasing the injected carrier density from 5 × 1017 to 2 × 1018 cm−3, the optical gain increases from 8.65 × 103 to 6 × 104 cm−3. Likewise, the radiative current density magnitude rises from 14.41 to 133.7 A/cm2. The same behavior was observed by Liu et al. [32]. They indicated an enhancement in optical gain varying the carrier concentrations from 8 × 1018 to 2.4 × 1019 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. They showed that optical gain in GaAsSbN/GaAs QW structures is about 2.8 × 103 cm−3, which is higher than GaAsSb/GaAs QW. They 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 GaAs0.35Sb0.65 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 × 1018 to 6 × 1018 cm−3.Figure 2
Optical gain and radiative current density as function of injected carriers densityNinj ranging from 5 × 1017 to 2 × 1018 cm−3 for p-GaAs/i-GaN0.38yAs1–1.38ySby/n-GaAs QW structure. The Sb composition and well width are ySb=18.6% and Lw=4nm, respectively.The calculated optical gain for doped GaNAsSb well for p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs quantum well laser is shown in Figure 3. It was significantly enhanced from 4 × 103 to 9.6 × 103 cm−3 with increasing doping density from 5 × 1016 to 1.5 × 1017 cm−3. Similarly, Kim et al. [21] reported the increase of optical gain as function of doping densities of the GaSb0.24As0.76/In0.26Ga0.74N0.06As0.94/GaAs QW structure. They 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. They indicated that at low strain level, the optical gain could be enhanced when n-type doping concentration increases from 5 × 1018 to 5 × 1019 cm−3. On the other hand, Huang et al. [38] studied the variation of maximum gain of Ge0.9375–mSn0.0625Pm, Ge0.9375–mSn0.0625Asm, Ge0.9375–mSn0.0625Sbm, and Ge0.9375–mSn0.0625Bim as a function of doping concentration for an injected carrier density of 1 × 1019 cm−3. They 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.Figure 3
Optical gain as function of energy for different doping densities for p-GaAs/i-GaN0.38yAs1–1.38ySby/n-GaAs QW laser structure with ND equal to 5 × 1016, 1 × 1017, and 1.5 × 1017 cm−3. The Sb composition and well width are ySb=18.6% and Lw=4nm, respectively.We investigated the effect of the applied electric field on the radiative current density for p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs QW structure operating at 1.55 µm telecommunication wavelength, as shown in Figure 4. The antimony composition and well thickness are ySb=18.6% and Lw=4.1nm, respectively. The calculated radiative current increases from 67.07 to 102.64 A/cm2 when F changes from 0 up to 40 kV/cm. This 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/cm2, with increasing the electric field from 0 up to 40 kV/cm. The rise of the current density is also indicated by Mensfoort et al. [40] for blue polymer-based light-emitting diodes. They interpret this increase by the improvement of the net space charge density caused by the reduced recombination rate for small voltages.Figure 4
The radiative current density as function of applied electric field F varying from 0 up to 40 kV/cm for p-GaAs/i-GaN0.38yAs1–1.38ySby/n-GaAs QW structure operating at 1.55 μm telecommunication wavelength. The Sb composition and the well width are ySb=18.6% and Lw=4.1nm, respectively.The radiative current densityJrad as well as the fundamental transition energy as function of well width Lw is shown in Figure 5(a). Jrad increases from 37.81 to 151.04 A/cm2. The increase of Lw 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 Te1-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 ySb for each used value of well width Lw. The optimized values of ySb are, respectively, equal to 17.8 and 18.8% for 4 and 4.5 nm, as shown in Figure 5(b). The radiative current density varies 47 from to 144.7 A/cm2 at 1.55 μm telecommunication wavelength.Figure 5
(a) Variation of radiative current density and fundamental energy transition as function of well width. (b) The adjusted value of Sb composition and radiative current density at 1.55μm.
(a)(b)Such optimization of the well parameters (well thickness and Sb composition) seems to be interesting investigation to enhance the optoelectronic performance of 1.55μm p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs quantum wells emitters.


## 4. Conclusion

The optoelectronic properties of 1.55μm p-GaAs/i-GaN0.38yAs1-1.38ySby/n-GaAs quantum wells were theoretically investigated using a self-consistent calculation combined with an anticrossing model. The maximum of gain is enhanced with increasing the injected carrier density. The optical gain reaches the value 9.6 × 103 cm−1 for doping density equal to 1.5 × 1017 cm−3. Moreover, the applied electric field significantly affects the radiative current density of the studied structure. The radiative current density is about 151.04 A/cm2 for 4.5 nm well width. The fundamental transition energy Te1-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.



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