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Abstract
A novel active region design based on a type-II InGaAs/GaAsSbBi quantum wells on GaAs substrate is proposed and studied in this work. The band structures of the InGaAs/GaAsSbBi type-II quantum wells are studied based on a self-consistent 14-band k·p model. The electronic and optical properties of dilute-bismide InGaAs/GaAsSbBi type-II quantum well structures are investigated theoretically. Moreover, the room temperature gain characteristics of the laser active region are studied with different Bi composition. The theoretical results indicate that adding Bi into InGaAs/GaAsSb type-II active regions on GaAs substrate extends the laser emission wavelength beyond 1550nm without sacrificing the peak gain value. It is shown that these type-II quantum well structures are suitable for 1550nm wavelength region operation at room temperature.
© 2017 Optical Society of America
1. Introduction
Laser diodes operating at 1550nm wavelength region are the key components for optical fiber communication. The InP based materials have been developed for 1550nm wavelength region laser application for decades. The conventional active region for 1550nm wavelength operation on InP substrate is based on InGaAs or InGaAsP quantum wells (QWs) structure. However, it is a challenge to achieve high quality Distributed Bragg Reflectors (DBRs) on InP substrates due to the lack of the high refractive index contrast lattice matched materials on InP substrate. Therefore, it is desirable to explore alternative active region layer materials on GaAs substrates to achieve 1550nm emission wavelength, since lattice matched DBR materials can be easily accessed on GaAs substrate.
The GaAs based laser diodes have drawn significant attention over years for 1300nm-1550nm wavelength region operation. Active regions of highly strained InGaAsN QWs [1], GaAsSb QWs [2], InAs quantum dots [3] and InGaAs/GaAsSb type-II QWs [4] were used to achieve 1300nm emission wavelength. However, it is still very challenging to extend the emission out to 1550nm wavelength region with these methods. Dilute-nitride type-II InGaAsN-GaAsSb QWs and type-I GaInNAsSb QWs structures were proposed and demonstrated to be the promising new materials to achieve laser emission at 1550nm on GaAs substrate [5–10]. Inducing N into InGaAsN layer can reduce the overall compressive strain of type-II QWs, which provides benefits for material growth. However, degraded optical efficiency and laser performance with increase emission wavelength have been observed with the increase in nitrogen concentration [11]. So far, the best performance lasers on GaAs substrate with longest wavelengths at the lowest threshold current have been achieved by Seth Bank’s group with GaInNAsSb QWs as active region [8].
Recently, dilute bismide materials have attracted intensive interests for variety of applications such as photodiodes, laser diodes, spintronics and thermoelectrics, due to their large band gap bowing effect [12,13]. It has been shown that the band gap decreases rapidly (60-88meV/ Bi%) with increasing bismuth fraction in GaAsBi [13]. In addition, GaAsBi materials with Bi composition larger than 10% would have the spin orbit splitting energy even larger than the band gap. These impact of Bi incorporation on the III-V material properties has the potential to lead to the suppression of the non-radiative conduction-heavy hole spin-orbit hole (the so called “CHSH” process) type Auger recombination loss in laser applications [14,15], which makes dilute bismide materials of significant interest for GaAs based lasers. Many works focus on developing high quality GaAsBi material system to push the lasing wavelength to 1300nm-1550nm range. So far, electrical pumped laser with emission wavelength up to 1060nm has been demonstrated with GaAsBi QWs [16], however, extension to 1550nm wavelength requires high Bi fraction (>10%), which is difficult to grow with high quality. Recent works on the type-II InGaAs/GaAsBi and GaAsBi/GaAsN QWs showed that these structures may provide a promising new material system for optoelectronics device applications on GaAs substrate. The InGaAs/GaAsBi type-II QWs show some potentials with emission wavelength out to 1300nm based on the photoluminescence results and simulation results. Further extending the emission wavelength to 1550nm has not been achieved yet. GaAsBi/GaAsN QWs have been demonstrated recently with photoluminescence emission peak wavelength of 1720nm, however, the epitaxial growth both dilute bismide and dilute nitride materials in QWs is expected to be very challenging.
In this paper, the novel InGaAs/GaAsSbBi type-II quantum well structures for laser application on GaAs substrate are proposed and studied, which show potentials to extend the emission wavelength out to 1550nm. It is shown in this work that incorporating Bi into GaAsSb layer instead of GaAs will require much less Bi content to achieve 1550nm emission wavelength. InGaAs/GaAsSbBi type-II quantum well structures were initially proposed on InP substrates for mid-infrared laser application. Here, these QWs are investigated for 1550nm wavelength region laser application on GaAs substrate. The comprehensive theoretical analysis of the optical properties of dilute InGaAs/GaAsSbBi QWs are presented, using a 14-band k·p Hamiltonian for GaAsSbBi and related alloys.
This paper is organized as follows. In section II, the theoretical model and material parameters for the dilute bismide type-II quantum well as the active region of lasers are presented. In section III, the momentum matrix elements characteristics of dilute-bismide QWs will be discussed. The effects of the Bi composition and Sb composition on the optical gain performance of type-II quantum well lasers are illustrated. Finally, section IV summarizes the paper.
2. Theoretical modeling and material parameters
In this section, the description of theoretical approach to determine electronic band structure of III-V-Bi is presented. The valence band anti-crossing (VBA) model is used to describe the interaction between Bi atoms and group V elements. The model assumes that the bismuth atoms substituted into group V elements are randomly distributed in the crystal lattice and weakly coupled to the extended states of the host III-V matrix. These bismuth atoms create a set of spin-degenerate heavy hole (HH), light hole (LH) and spin orbit (SO) like Bi-related localized states which interact with the valence band of host material [1]. To calculate the band structure of InGaAs/GaAsSbBi type-II QWs laser structure, the 14-band k·p Hamiltonian is used to describe GaAsSbBi, which extends from typical 8-band Hamiltonian including the spin-degenerate conduction band (CB), HH, LH and SO valence band of the host matrix. The six Bi-related localized states in the 14-band k·p Hamiltonian couple to the valence band through a composition-dependent valence band anti-crossing interaction. This type of band anti-crossing model is similar to the 10-band k·p Hamiltonian to describe the dilute nitride alloys such as InGaAsN QWs. In dilute nitride alloys, the N atoms introduce resonant state in the conduction band of III-V host [2], while Bi atoms introduce resonant states below the valence band edge in the dilute bismide alloys.
The quantum well energy band structures are calculated in the axial approximation via 14 × 14 diagonalized k·p Hamiltonian matrix as shown in the previous work [3] In this work, to model the gain characteristics more accurately, self-consistent modeling including carrier screening effect is used to solve the k·p equation and Poisson’s equation simultaneously. The finite difference method is used to solve the k·p equations. The spatial interval for the finite difference method is 1. The band-edge potential is solved self-consistently due to the coupling of the carrier distribution and band-edge potential. The iteration loop of solving the k·p equations and Poisson’s equation alternately is formed until the potential converges (the Euclidean norm of the potential vector difference is less than 1e-3 eV). Once the solution converges, the optical gain of the quantum well can be derived from Fermi’s golden rule according to the literature [4].
In this paper, GaAsP/InGaAs/GaAsSbBi/InGaAs/GaAsP QW structure is discussed with the band diagram shown in Fig. 1. The 10nm GaAsP surrounding the QW is used as barrier to improve the carrier confinement and wave function overlap between electron and hole, which is critical for type-II QWs laser design. Moreover, the GaAsP layer is tensile strained, and can be used to compensate the compressive strain in InGaAs and GaAsSbBi layers [5], which will give more degree of freedom for designing the InGaAs/GaAsSbBi QW. It is also noted that GaAsP is not the only option as barrier for carrier confinement, AlGaAs could be another candidate as barrier for active region design. High Al content AlGaAs could offer good carrier confinement as well. Since this work focus on the design of InGaAs/GaAsSbBi layers, GaAsP barriers layer is used for the following analysis.
The Bi-free material parameters such as the lattice constant, band gaps, conduction band offsets, and elastic constants are based on the review literature [6]. The parameters of ternary material are calculated by using the linear interpolation between the parameters of the relevant binary semiconductors with bowing effect included. The parameter of GaAsSbBi such as Luttinger parameters and electron effective mass are assumed to be the same as the Bi-free GaAsSb with the same Sb composition at approximation. The energy positions of Bi-related levels and the VBAC coupling parameters of GaAsSbBi alloy are not available in experimental results, but very critical for determining the band structure of QWs. The same strategy to get these values is utilized as the previous work [3]. The energy positions of Bi-related levels and the VBAC coupling parameters of GaAsSbBi alloy is linearly interpolated from these parameters in GaAsBi and GaSbBi alloys parameters [1,7,8]. In GaAsBi material, the energy positions of HH and LH like Bi-level are 0.183eV below the valence band, and the VBAC coupling parameter is 1.13eV as shown in recent paper [7]. In GaSbBi material, the HH and LH like Bi-related energy level is 1.17eV below GaSb and the VBAC coupling parameter is 1.1eV [8]. It is noted that Bi-related energy levels in GaAs are much closer to valence compared to the case in GaSb, which causes the band gap reduction per %Bi to be larger in GaAs than that of GaSb. For the GaAs0.65-xSb0.35Bix alloy used in this paper, it is assumed that the energy positions of HH and LH like Bi-level are 0.528eV below the valence band edge of GaAsSb, the SO like Bi-level is 1.9eV below the valence band edge, and the VBAC coupling parameters are 1.12eV, based on the linear interpolation of GaAs and GaSb case. It is noted the SO-like localized states lie well below the valence band edge, which have little impact on the valence states and can be ignore [7]. In this paper, 14 band k·p is still used to include these SO-like localized states to keep the model more general for other applications. The conduction band offset of GaAs0.65-xSb0.35Bix changes by 28meV as Bi composition increases by 1%, and this value is also linearly interpolated from GaAsBi and GaSbBi alloys [8–10]. While these parameter remains somewhat controversial, the uncertainty affects only the details and not the main qualitative trend of the simulation study in this work. The material parameters used in this work are listed in Table 1.
Table 1. Parameters of the Constituent Materials in the InGaAs/GaAsSbBi QW used for the 14 Band k.p Calculations
3. Modeling results
In order investigate the potential application of InGaAs/GaAsSbBi QWs for 1550nm wavelength emission, different In mole fraction in InGaAs and Sb mole fraction of GaAsSb should be studied first for Bi-free structures. Figure 2(a) and 2(b) illustrate the contour plot of the calculated transition wavelength and wave function overlap between electron and hole ground state for varying In content in InGaAs layers and Sb content in GaAsSb layer. The right upper corner of the Fig. 2(a) and 2(b) beyond the red dot line may be inaccessible in practice due to the limit of excessive strain. These impacts on the optical properties of type-II QWs were also consistent with the study carried out by Luke J. Mawst’s group [11]. It is found that in order to achieve wavelength beyond 1.55, very high In content and Sb content (>40% or more) are necessary. It would be challenging to grow QW on GaAs substrate with such high compressive strain. In this work, a novel material GaAsSbBi with dilute Bismide is proposed and studied for 1.55 wavelength emission application, which can extend the emission wavelength without significant increase of the compressive strain in QW.
Fig. 2 Contour plot of (a) transition wavelength and (b) wave function overlap of 3nm InGaAs/3nm GaAsSb/3nm InGaAs type-II “W” QW structure at 300K, versus In content in InGaAs and Sb content in GaAsSbBi. The red dot lines in both figures indicate the boundary where the total 9nm QW thickness is equal to the critical thickness with the corresponding strain in the QW. Beyond the red dot line in right upper corner, the total thickness of QW would be larger than the critical thickness of structure.
Here, the In content of InGaAs is fixed to be 34%, and Sb content of GaAsSb is fixed to be 35%. These contents can easily be realized without strain relaxation in the QW system with thickness of 25 −35 based on experimental work from reference [5]. The GaAs0.85P0.15 layer is used as a barrier to compensate the compressive strain in QWs in the simulation, which was shown to improve the photoluminescence intensity at room temperature due to the better carrier confinement [5]. From a growth perspective, the 10nm GaAs0.85P0.15 barrier layers is still well below the critical thickness of GaAs0.85P0.15, which have been demonstrated experimentally to grow on GaAs substrate as a barrier for the similar type-II InGaAsN/GaAsSb structures [12]. The influences of Bi content on the electronics band structure and optical property of the type-II QWs will be studied in this work.
The conduction band and valence band energy dispersion of 3nm In0.34Ga0.66As/3nm GaAs0.65-xSb0.35Bix/3nm In0.34Ga0.66As QWs with Bi mole fraction of 0%, 3% and 5% were calculated respectively, as shown in the Fig. 3(a) and 3(b). It is known that thicker QW layer can help extend the transition wavelength in these “W-type” QWs, but at the cost of weaker optical transition strength, which would decrease the optical efficiency in laser structures [13,14]. In this work, such thin QW layers is chosen to improve the spatial wave function overlap between electrons and holes in adjacent layers. In Fig. 3, C1 and C2 are the symmetrical and anti-symmetrical states of the two coupled quantum wells in the conduction band, and HH1 and HH2 are the first and second valence subband for heavy hole. The effective bandgap (transition energy difference between lowest bound electron state C1 and the highest energy bound hole state HH1), energy differences of C2-C1 and HH1-HH2, the effective mass of C1 electron and HH1 hole are calculated based on the energy dispersion relationship in Fig. 3. It is shown in Table 2 that the effective bandgap of the “W” QWs decrease from 0.8773eV in the Bi-free QWs to 0.7526eV in the 5% GaAsSbBi case. This is due to the VBAC-induced upward shift of valence band edge energy in GaAsSbBi material. It is noticed that the effective bandgap reduction per %Bi in these type-II QWs is less than the typical value in GaAsSb alloy based on linear interpolation from GaAs and GaSb materials. That is mainly due to the fact that the conduction band edge of InGaAs and valence band edge of GaAsSbBi are the main factors to determine the effective bandgap of type-II QWs, but not the conduction band edge of GaAsSbBi. Therefore, the downshift of conduction band edge of GaAsSbBi has very little impact on the effective bandgap in the type-II QWs. Moreover as shown in Table 2, the conduction subband separation increases from 24meV to 30.8meV as the Bi composition increases to 5%. In the InGaAs/GaAsSbBi type-II quantum well, higher Bi fraction will lower the conduction band edge of the GaAsSbBi layer, which causes the two InGaAs electron QWs coupled more to each other. Thus, the conduction subband separation increases as Bi fraction increases. On the other hand, the valence subband separation between HH1 and LH1 also increases as Bi composition increases. That is due to the fact that GaAsSbBi well becomes deeper for holes as Bi fraction increases. These trends will help to achieve population inversion in type-II QW and are also similar to that of the dilute Bismide type-II “W” QW structure on InP substrate [3]. Moreover, the effective mass of C1 and HH1 slightly increases as Bi fraction increases as indicated in Table 2.
Fig. 3 The energy dispersion of the “W” In0.34Ga0.66As/3nm GaAs0.65-xSb0.35Bix/3nm In0.34Ga0.66As QWs with Bi mole fraction of 0%, 3% and 5%. (a) conduction band energy dispersion (b) valence band energy dispersion, where C1 and C2 refer to symmetric and anti-symmetric conduction subband, HH1 and LH1 refer to the first confined state of heavy hole and light hole subbands.
Table 2. Effective Bandgap, Energy Differences of C2-C1 and HH1-HH2, and Effective Mass of C1 Electron and HH1 Hole
Figure 4 illustrates the TE and TM component of the squared momentum matrix element as a function of the in-plane wave vector k// for transitions between C1 and HH1 for 3 nm InGaAs/3 nm GaAsSbBi QW with different Bi fractions. As indicated in Fig. 4, it is obvious that the C1-HH1 transition contributes only to the TE polarization with E field parallel to the layers near the zone center. The matrix element decreases as the in-plane wave vector magnitude k// increases. That is due to the fact that heavy hole and light hole bands begin to mix as in-plane wave vector magnitude moves away from the zone center. Similarly, transverse magnetic (TM) component of the matrix element rises slightly around the middle of the Brillouin zone. Moreover, it is shown that as Bi fraction increase from 0% to 5%, the squared momentum matrix element increases. This trend is different from the trend reported in dilute Bi (<6%) GaAsBi/AlGaAs type-I quantum well laser structure [15]. In GaAsBi/AlGaAs type-I QW structures, the optical matrix elements decrease when the Bi increase from 0% to 6% due to the hybridization of bound hole states with Bi-related state. By further increasing Bi content in type I QW, optical matrix elements begin to increase due to the increased conduction band offset and electron confinement. In contrast, for type-II QWs, even though the hybridization of bound hole states with Bi-related localized states could reduce the wave function overlap between the bound electron and hole state, on other hand, the Bi in GaAsSbBi can lower the conduction band edge of GaAsSbBi, and thus increases the wave function overlap. These two mechanisms compete and determine the trend as Bi fraction increases in QWs. In type II QWs, the wave function overlap can increase rapidly as the conduction band of GaAsSbBi decreases, and the latter mechanism wins in these GaAs based InGaAs/GaAsSbBi type-II QWs based on the simulation results shown in Fig. 4. This phenomena is not seen type-II dilute N InGaAsN/GaAsSb QWs as well. This improvement of the squared momentum matrix element may offer a potential direction for improving the optical transition efficiency and shows advantages over other QWs structure on GaAs substrate.
Fig. 4 The TE and TM component of the squared momentum matrix element of the C1-HH1 transition for the Bi composition of 0%, 3% and 5% for 3nm InGaAs/3nm GaAsSbBi.
The material gain curves (TE mode) for one 3nm In0.34Ga0.66As/3nm GaAs0.65-xSb0.35Bix/3nm In0.34Ga0.66As QW with various Bi concentrations are calculated using flat band method as shown in Fig. 5 with different carrier density. It is noted that gain versus current density could be more helpful to compare with experimental data, however, it is difficult to predict the current density versus carrier density in active region, since the role of non-radiative recombination in the dilute-bismide material is not well understood. The gain value of TM mode is neglected in the analysis. The TE gain with carrier concentration of 2 × 1018 cm−3,4 × 1018 cm−3, and 6 × 1018 cm−3 were calculated. As displayed in Fig. 5, the peak gain wavelength increases from around 1.38µm to 1.61µm as Bi content increases from 0% to 5%. The gain values calculated in Fig. 5 are slightly lower than the typical InGaAs/InP type-I quantum well laser, but are sufficient to satisfy the requirement for laser operation [16]. It indicates that InGaAs/GaAsSbBi type-II QWs are very promising for GaAs-based lasers operating at 1550nm wavelength region.
Fig. 5 The calculated TE material gain spectra for 3nm InGaAs/3nm GaAsSbBi QW with Bi composition of 0%, 3% and 5% and carrier concentration of 2 × 1018 cm−3, 4 × 1018 cm−3, and 6 × 1018 cm−3. The solid curve is for Bi-free QW, the dashed curve is for 3% Bi QW and dotted curve is for 5% Bi QW.
To further illustrate the advantage of InGaAs/GaAsSbBi type-II QWs over InGaAs/GaAsBi type-II QWs,the simulations with different Sb composition in dilute Bi type-II QWs structures were carried out. Figure 6 show the impact of the Sb composition in InGaAs/GaAsSbBi type-II QWs with Bi mole fraction of 5%. In Fig. 6, as Sb content in GaAsSbBi QW changes from 0% to 35%, it shows the peak gain wavelength extend dramatically from around 1070nm to around 1610nm. In the InGaAs/GaAsBi type-II QW, 5% Bi mole fraction can only extend the emission wavelength to around 1070nm. In other word, in order to achieve the emission wavelength beyond 1550nm, very high Bi fraction (>10%) is required. In that case, the QW itself is no longer type-II because the conduction band edge of high Bi fraction GaAsBi layer is lower than that of InGaAs layer. It is worth noting that the optical quality of dilute bismide alloy deteriorates with the increase in bismide concentration. In contrast, the GaAsSbBi proposed in this work requires much less Bi fraction to achieve 1550nm emission wavelength, which would be more promising in laser applications.
Fig. 6 The calculated TE material gain spectra for 3nm InGaAs/3nm GaAs0.95-ySbyBi0.05 QW with Sb composition 0%, 20%, 35% and carrier concentration of 2 × 1018 cm−3, 4 × 1018 cm−3, and 6 × 1018 cm−3. The solid curve is for Sb-free QW, the dashed curve is for 20% Sb QW and dotted curve is for 35% Sb QW.
To model these GaAs based type-II QW structures more accurately, the self-consistent model is utilized to calculate the optical gain characteristics, which includes the impact of the accumulation of electrons and holes in the QW. In Fig. 7, the energy dispersion curves are plotted for two conduction subbands (C1 and C2) and two valence subbands (HH1 and HH2) with flat band model and self-consistent model. Comparing the band structure for two methods at an injected carrier density of 6 × 1018 cm−3, it is found that the trend of subband dispersion is not affected, but the subband energies are pushed downwards for both electron band and hole band due to the band-bending effect. The shift of the conduction subband is not as much as that of the valence subband due to the larger effective mass of hole in the valence band. Moreover, the comparison of TE gain characteristics using flat band and self-consistent model is shown in Fig. 8. According to Fig. 8, the peak gain calculated is higher and the peak gain wavelength is shorter with the self-consistent model because the band bending induced by the screening carriers leads to a larger effective bandgap and larger wave function overlap. Moreover, the blue shift of gain peak as the injected carrier density increases is observed in the self-consistent model, which is also due to the screening potential.
Fig. 7 The energy dispersion of the “W” In0.34Ga0.66As/3nm GaAs0.65-xSb0.35Bix/3nm In0.34Ga0.66As QWs with Bi mole fraction of 5%. (a) conduction band energy dispersion (b) valence band energy dispersion with both flat band model and self-consistent model with injected carrier density of 6 × 1018 cm−3.
Fig. 8 The calculated TE material gain spectra for 3nm InGaAs/3nm GaAsSbBi QW with 5% Bi fraction and carrier concentration of 2 × 1018 cm−3, 4 × 1018 cm−3, and 6 × 1018 cm−3. The solid curve is for flat band model, the dashed curve is for self-consistent model.
All these potential advantages of the InGaAs/GaAsSbBi QWs indicate these structures are ideal candidates as the active region for 1550nm emission wavelength laser on GaAs substrate, which could motivate future experimental studies of GaAsSbBi on GaAs substrate, even though the growth of the GaAsSbBi materials on GaAs substrate may be challenging.
4. Conclusion
In this work, a novel alternative active region based on the type-II transition of InGaAs/GaAsSbBi QWs was proposed and studied with the self-consistent 14 × 14 k·p model. The band structure and optical gain of InGaAs/GaAsSbBi type-II “W” quantum well have been calculated as a function of Bi fraction. The incorporation of Bismide into GaAsSb layer in type-II QW shifts the gain peak from 1.38 to 1.61µm with the increase of Bismide composition from 0 to 5%. The squared momentum matrix element increases as Bi fraction increases, which allows for larger gain in QWs. It is also shown that using GaAsSbBi layer instead of GaAsBi to build type-II QWs requires much less Bi fraction to achieve 1550nm emission wavelength laser on GaAs. The theoretical studies indicate that the InGaAs/GaAsSbBi QW is a very promising material system to realize GaAs based 1550nm emitting laser diodes.
Funding
Shanghai Sailing Program (No. 17YF1429300), Shanghai Tech University startup funding (No. F-0203-16-002)
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