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Abstract
To obtain high performance of GaN-based laser diodes (LDs), three series of LDs are proposed, the effects of Al content of p-AlGaN cladding layer, as well as the material composition and thickness of upper waveguide layer (UWG) are investigated separately. As the Al content increases, the threshold current and output power are found to improve significantly. Meanwhile, the optical field distributed on the p-type side is reduced. Besides, the photoelectric characteristics of LDs are further improved when In0.03Ga0.97N/In0.01Ga0.99N UWG is used. Moreover, proper choice of the In0.03Ga0.97N/In0.01Ga0.99N UWG thickness is necessary to achieve the high performance of GaN-based LDs.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
GaN-based semiconductor materials are the preferred materials for manufacturing high-performance optoelectronic devices such as laser diodes (LDs), photo-detectors and light-emitting diodes (LED) due to their good thermal stability, strong corrosion resistance, wide adjustable band gap and high electron saturation rate [1–3]. In recent years, with the technological breakthroughs in GaN-based material growth, structure design and manufacturing process, GaN-based LDs have attracted more attention because they have bright application prospects in the fields of laser display, micro portable projectors, atomic clocks, communication systems, medical instrument and high-density optical data storage [4–7]. Nevertheless, the slope efficiency of GaN-based LDs is much smaller than that of GaAs-based LDs because of the large absorption loss [8,9]. Generally, optical loss has a significant impact on the performance of GaN-based LDs such as threshold current, slope efficiency [10]. One reason for the large absorption loss is the Mg-doped p-type layer with high absorption coefficient [11]. The high absorption coefficient is attributed to the large ionization energy of the Mg-doped p-(Al)GaN material, and the ionization energy increases with the increase of the Al composition [12,13]. The probability of Mg atoms being ionized into free holes is very low, less than 10%, while most of them form acceptor-bound holes, resulting in large internal optical loss [14–16]. Another reason is the refraction or reflection of light inside the gain medium due to the inhomogeneous compositions or the non-uniform distribution of carriers, which makes part of the light wave deviate from the original propagation direction and causes optical loss [17]. Besides, the lack of lattice-matched substrates in the epitaxial growth leads to more defects in the crystal, which can act as non-radiative recombination centers and generate heat by consuming the injected carriers, thus causing scattering loss and reducing the internal quantum efficiency and reliability of GaN-based LDs [18,19].
Considering the high loss of GaN-based LDs due to the above reasons, this paper aims to obtain the high performance of GaN-based LDs by designing and optimizing the LD structures. We propose three series of different structures, namely the variation of Al composition in p-type AlxGa1-xN cladding layer (p-CL), the material and thickness in upper waveguide layer (UWG), and investigate them systematically by simulation using LASer Technology Integrated Program (LASTIP) [20]. We found that when Al composition in p-CL increases, the optical field can move away from the p-type side and the full width at half maximum (FWHM) is obviously reduced. Meanwhile, the output power and threshold current can be improved. However, considering that high Al composition increases the difficulty of growing high-quality p-type layers, the Al composition in p-CL is not recommended to be too high. Subsequently, we optimize the design of UWG material of GaN-based LDs based on a fixed Al content of p-CL of 6%. The In0.03Ga0.97N/In0.01Ga0.99N UWG is found to be more conducive to improve the optical and electrical properties of LDs than the conventional GaN UWG and InGaN UWG. Additionally, the influence of thickness of In0.01Ga0.99N in In0.03Ga0.97N/In0.01Ga0.99N is also analyzed.
2. Methods
To achieve high performance of laser diodes, three series of GaN-based LD structures are proposed and analyzed. The schematic diagram is shown in Fig. 1. The original structure in our simulation is grown on a GaN substrate, which consists of a 1-µm thick n-type GaN layer (Si: 3×1018 cm−3), a 1-µm thick n-type Al0.08Ga0.92N cladding layer (n-CL) (Si: 3×1018 cm−3), a 0.12-µm thick n-type In0.02Ga0.98N lower waveguide layer (LWG) (Si: 1×1018 cm−3), an active region with two In0.2Ga0.8N quantum wells (QWs) and three GaN quantum barriers (QBs), a 0.12-µm thick unintentionally-doped GaN upper waveguide layer, a 20-nm thick p-type Al0.2Ga0.8N electron blocking layer (EBL) (Mg: 5×1019 cm−3), a 600-nm thick p-type Al0.06Ga0.94N cladding layer (Mg: 5×1019 cm−3), and a 40-nm thick p-type GaN contact layer (Mg: 1×1020 cm−3). To be closer to the experiment, the cavity length of the device is 600 µm and the ridge width is 3 µm. In series I, we design p-CL with Al composition varying from 0.01 to 0.1 to investigate the effect of the Al content on performance of GaN-based LDs. Except for p-CL, the parameters of other layers are fixed and the same as the original structure. Then, based on the Al0.06Ga0.94N p-CL in original structure and series I, the material and thickness of the upper waveguide layer are investigated to further optimize the LD structures. In series II, four upper waveguide layers with different materials are designed, namely GaN (LD1), In0.01Ga0.99N (LD2), In0.03Ga0.97N (LD3), and In0.03Ga0.97N/In0.01Ga0.99N (LD4). The total thickness of UWG is 120 nm for four structures, and in LD4 the In0.03Ga0.97N/In0.01Ga0.99N UWG thickness is 70/50 nm. In series III, the UWG of all structures is composed of In0.03Ga0.97N/In0.01Ga0.99N, where the thickness of In0.03Ga0.97N is 70 nm and the thickness of In0.01Ga0.99N varies from 30 to 550 nm.
Fig. 1. Schematic diagram of series I, II, and III samples. In series I, the Al content in p-type AlxG1-xN cladding layer (p-CL) varies from 0.01 to 0.1. In series II, the materials of the upper waveguide layer (UWG) are GaN, In0.01Ga0.99N, In0.03Ga0.97N, In0.03Ga0.97N/In0.01Ga0.99N, respectively. In Series III, the thickness of In0.01Ga0.99N layer in In0.03Ga0.97N/In0.01Ga0.99N UWG varies from 30 nm to 550 nm.
The LASTIP simulation program is employed to calculate the three series of structures. It uses the finite element method to solve the Poisson's equation, the Schrödinger equation, the scalar wave equation, and the current continuity equation to analyze the photoelectric properties of LDs, such as P-I-V curve, energy band, carrier distribution and optical field distribution [20,21]. For accurate simulation, the operating temperature is set to 300 k. The screening factor is set to 0.25 due to the partial compensation of built-in polarization by defects and other interface charges [22]. Furthermore, the band gap energies of InGaN and AlGaN materials are calculated at room temperature by the following formulas [23]:
In addition, during the calculation, a relatively high value of absorption loss of p-type layers is taken deliberately in order to make the three series of LDs satisfy the high loss condition, in this case, the effect on device performance can be more pronounced when the p-CL and UWG are designed so that the distribution of the optical field deviates from the p-type region, i.e., the absorption coefficient of all p-type layers is assumed to be 200 cm−1. Besides, the absorption coefficient of all n-type layers is 5 cm−1[11]. Meanwhile, both n-type and p-type electrodes are assumed to be ideal ohmic contacts.
3. Results and discussion
3.1 AlxGa1-xN p-CL
The effect of Al composition in p-CL on the performance of GaN-based LDs is investigated first. Figure 2(a) plots the optical field distribution of 10 p-CL structures with varying Al composition. It is found that the optical field moves away from the p-type region with the increase of Al content. Figure 2(b) shows the FWHM and optical field centers of the spatial distribution of the optical field for the 10 p-CL structures. Moreover, the center of optical field (COF) shifts from MQWs to LWG and the FWHM decreases from 358 nm to 310 nm when the Al composition rises from 1% to 10%. To find out the reason, the optical confinement factor and optical loss as a function of Al content in p-CL are illustrated in Fig. 2(c), where the optical confinement factor is calculated from n-GaN to p-GaN region. Apparently, the optical confinement factor increase slightly from 1.2% to 1.4% when the Al content changes from 1% to 10%. Meanwhile, the optical loss reduces significantly from 62.3 cm−1 to 32.3 cm−1 with the rise of Al content. Generally, the variation of Al composition is closely related to the refractive index of AlGaN materials. Furthermore, with the increase of Al content, the refractive index of AlxGa1-xN p-CL decreases, which means that the refractive index contrast between p-CL and UWG increases. A larger refractive index contrast causes the optical field to move away from the p-type side, and the optical field confinement ability is enhanced, so the FWHM decreases and the optical confinement factor increases. Correspondingly, the optical loss decreases with the increase of Al composition due to the reduction of the optical field distributing in the p-type side with high absorption loss. Therefore, the Al content in p-CL has a remarkable effect on the optical properties of GaN-based LDs.
Fig. 2. The dependencies of (a) optical field distribution, (b) center of optical field (COF) and full width at half maximum (FWHM) of the optical field, and (c) optical confinement factor and optical loss on the variation of Al composition in p-CL.
Figure 3(a) exhibits the output power and voltage versus injection current (P-I-V) curves for series I. The turn-on and forward voltages are found to be approximately the same for all structures as the Al content rises from 1% to 10%, indicating that the variation of the Al composition in the p-CL has little effect on the resistance of the device. In contrast, the slope efficiency and threshold current are obviously improved with the increase of Al content. For clearer observation, the output power at an injection current of 120 mA and threshold current are displayed in Fig. 3(b). It is obvious that the threshold current of p-CL structure with 10% Al content is the lowest among all the structures, and its threshold current is 28.6 mA, which is 43% lower than that of p-CL structure with 1% Al content. Moreover, the output power at 120 mA rises from 46.5 mW to 97.6 mW with the increase of Al composition. Actually, the threshold current density of the laser diodes can be described by [24]:
Where J0, ηi, and β0 denote the transparent current density, the internal quantum efficiency, and the gain coefficient, respectively. αt represents the total loss and Γ is the optical confinement factor. J0 and β0 are only related to the parameters of the active region and are considered as constants in our calculations [25]. According to Eq. (3), lowering the loss and increasing the optical confinement factor can favorably reduce the threshold current density of LDs, which explains why the threshold current decreases with increasing Al content.
Fig. 3. (a) The output power and voltage versus injection current (P-I-V) curves and (b) the dependencies of output power at 120 mA and threshold current on the variation of Al composition in p-CL.
In addition, the slope efficiency of LDs depends on the carrier injection efficiency(ηinj), the internal absorption loss (αi) and the mirror loss (αm), which can be expressed by [26]:
To understand another reason for the variation of slope efficiency, we analyze the conduction band diagram at an injection current of 120 mA and the effective potential barrier height of electrons at EBL, as displayed in Fig. 4. Here, the effective potential barrier height for electron is the difference between the conduction band and its Fermi energy level at a certain position. In general, electrons are injected into the MQWs from the n-type side and part of them may overflow from the active region caused by the small effective mass and large mobility. However, a large electron leakage can reduce the photoelectric conversion efficiency and lead to the performance degradation of device. It is observed that the conduction band at the EBL is significantly higher than that on either side of it. The bulging conduction band facilitates the suppression of electron spillover into the p-type region and alleviates the leakage of electrons. When the Al composition in p-CL is low, i.e., 1%, the effective barrier height of electrons at EBL is 449 meV. As the Al composition increases to 10%, the effective barrier height of electrons reaches 460 meV, as depicted in the inset of Fig. 4. The result indicates that increasing the content of Al in p-CL is beneficial to enhance the effective potential barrier height of electrons at EBL. A larger effective electron barrier height helps to reduce electron leakage and enhance the electron confinement ability of MQWs. As a result, more electrons and holes are involved in radiative recombination in the active region, which improves the carrier injection efficiency, and thus improves the output power and slope efficiency.
Fig. 4. Conduction band diagram at 120 mA. The inset in Fig. 4 shows the effective barrier height of electrons at EBL as a function of the Al content in p-CL.
It is noteworthy that although increasing the Al content in p-CL is beneficial to reduce electron leakage and enhance the optical and electrical properties of GaN-based LDs, it does not mean that a higher Al content is always better. Because the center of the optical field slowly deviates from the MQWs and moves toward the LWG as Al content rises (shown in Fig. 2(b)), resulting in a decrease of the optical field distributed in the MQWs. Additionally, AlGaN materials with high Al composition may generate a large number of dislocations during crystal growth due to the lattice-mismatch with substrate, which degrades the quality of the devices. Moreover, increasing the Al content in AlGaN layer will correspondingly aggravate the doping of the device, especially the p-type doping. In addition, many reports on the Al content of the p-AlGaN cladding layers are below 10% [27–29]. Consequently, considering the practical situation, the Al content in AlxGa1-xN p-CL should not be too high. To achieve the better performance of GaN-based LDs, further optimization of the LD structure is required.
3.2 In0.03Ga0.97N/In0.01Ga0.99N UWG
Subsequently, we study the material of the upper waveguide layer to optimize the structure of LDs. In this series of samples, i.e. LD1, LD2, LD3, and LD4 of series II, the Al content in AlxGa1-xN p-CL is chosen to be 6% in order to achieve a relatively high effective barrier height of electrons in EBL and a relatively small shift of the optical field center toward LWG, and the materials of UWG are GaN, In0.01Ga0.99N, In0.03Ga0.97N, In0.03Ga0.97N/In0.01Ga0.99N, respectively. Figure 5(a) depicts the P-I curves of the four structures. The output power of the four structures is found to be almost unchanged at low injection currents. However, with the increase of current, LD4 starts lasing at first, followed by LD1, LD2 and LD3. Correspondingly, the output power at 120 mA and threshold current are given in Fig. 5(b). The output power of LD4 at 120 mA is 82.5 mW, slightly higher than the 79.9 mW of LD1, 77.8 mW of LD2, and 75.1 mW of LD3. Moreover, the threshold current of LD4 is only 27.2 mA, while the values of LD1, LD2 and LD3 are 32.5 mA, 31.6 mA and 30.4 mA respectively. The results reveal that the UWG with In0.03Ga0.97N/In0.01Ga0.99N material facilitates the reduction of the threshold current and the increase of the output power, and thus the electrical performance of LDs is enhanced.
Fig. 5. (a) Output power versus injection current (P-I) curves and (b) output power at 120 mA and threshold current of four LDs.
As mentioned above, the leakage of electrons affects slope efficiency and output power of LDs, so the change of electron current density in LD active region of four LDs are examined at an injection current of 120 mA. From Fig. 6, the electrons injected from the n-type region recombine with the holes in the MQWs, resulting in a sharp decrease in the electron current density in each quantum well. In addition, it is found that the electron leakage current of LD3 is the largest and that of LD4 is the smallest, which is opposite to the trend of the output power shown in Fig. 5(b). Specifically, for LD1 with GaN UWG, the electron leakage current is about 577.9 A/cm2. For LD2 and LD3, the electron leakage currents are 649.6 A/cm2 and 825.8 A/cm2, respectively, being slightly higher than those of LD1. When In0.03Ga0.97N/In0.01Ga0.99N material is used as the upper waveguide layer, i.e. LD4, the electron leakage current is significantly reduced to 206.9 A/cm2. A smaller electron leakage current means that only fewer electrons leak out of the active region, and most of them participate in the radiative recombination. Therefore, LD4 has the largest output power among the four LDs.
Fig. 6. The distribution of electron current density in the active region of four LDs at an injection current of 120 mA.
The optical field distribution of the four structures, as well as their optical confinement factor and optical loss, are analyzed as shown in Fig. 7(a). The optical field shifts away from the n-type side when the GaN upper waveguide is replaced by the InxGa1-xN upper waveguide. The inset of Fig. 7(a) depicts the COF and FWHM of the four LDs. It is found that the COF of LD1 is located in the lower waveguide layer, and the other three LDs are located in MQWs. Besides, the FWHM of LD1, LD2, LD3, and LD4 are 324 nm, 317 nm, 294 nm, and 292 nm, respectively. The result demonstrates that the optical field is compressed and the FWHM is narrower when In0.03Ga0.97N/In0.01Ga0.99N UWG is used. This phenomenon may be attributed to the increase in the optical confinement factor, caused by the change of the UWG refractive index. From the curves shown in Fig. 7(b), the optical loss of LD4 is 42.8 cm−1, being lower than 45.3 cm−1 of LD3, slightly higher than 42.5 cm−1 of LD2 and 40.7 cm−1 of LD1. As aforementioned, the increase in optical loss is ascribed to the shift of optical field to the p-type side. In addition, there is an effect of competition between the optical confinement factor and the optical loss, where the optical constraint factor dominates. It may be the reason why the threshold current of LD4 shown in Fig. 5(b) is slightly lower than the other three LDs.
Fig. 7. (a) Optical field distribution and (b) optical confinement factor and optical loss of four LDs at 120 mA. The inset in Fig. 7(a) is the FWHM and center of optical field for four LDs.
3.3 Thickness of the In0.01Ga0.99N layer in In0.03Ga0.97N/In0.01Ga0.99N UWG
The results of series II samples suggest that the upper waveguide structure with In0.03Ga0.97N/In0.01Ga0.99N material contributes to improving the photoelectric performance of high-loss LDs. Nevertheless, the improvement is not very remarkable. Therefore, an adjustment of the thickness of In0.01Ga0.99N layer in In0.03Ga0.97N/In0.01Ga0.99N UWG is made, and the effect on performance of LDs is calculated.
Figure 8 illustrates the optical field distribution with the thickness varying from 30 nm to 550 nm. It is found that the optical field distributed in the n-type layer changes only slightly as the thickness rises, while the optical field distributed in the p-type side increases significantly. Furthermore, the FWHM increases from 288 nm to 404 nm and the COF pushes from MQWs to UWG when the thickness rises from 30 nm to 550 nm. In addition, as the thickness increases, the optical confinement factor and optical loss decrease from 1.6% to 1.1% and from 46.9 cm−1 to 9.2 cm−1, respectively. The reason for these phenomena may be that the light absorption capacity of UWG increases with the increase of thickness, leading to a broadening of the optical field toward the p-type side and a decrease of the optical confinement factor. Additionally, the increase of UWG thickness means that the distance between the active region and the p-type layer increases. Although the optical field moves toward the p-type side, most of the moving optical field is distributed in the UWG with smaller absorption coefficient, while the optical field distributed in the p-type layer with larger absorption coefficient is relatively reduced, so the optical loss decreases accordingly.
Fig. 8. (a) Optical field distribution, (b) FWHM and center of optical field, and (c) optical loss and optical confinement factor versus the thickness of In0.01Ga0.99N layer in In0.03Ga0.97N/In0.01Ga0.99N UWG at an injection current of 120 mA.
Figure 9 exhibits the P-I curves when the In0.01Ga0.99N layer thickness varies. Obviously, the threshold current first decreases and then rises as the thickness varies from 30 nm to 550 nm, and a minimum threshold of 23.9 mA is achieved at the thickness of 250 nm. The reason is similar to what was discussed in Fig. 7 above, which is probably attributed to the competition between the optical confinement factor and the optical loss as both of them decrease with increasing thickness. In contrast, at an injection current of 120 mA, the output power first rises and then drops with the increase of thickness, and the maximum value of 157.6 mW is obtained at a thickness of 400 nm. Actually, the increase in UWG thickness implies an increase in the transport distance of the holes to the active region. When the thickness is thin, the effect of UWG on the hole injection is not significant. However, with a large increase of the thickness, the difficulty of hole’s transport increases, resulting in a decrease of hole current density injected into MQWs, thereby reducing the radiative recombination of carriers. This may be the reason why the output power enhances first and then decreases as the thickness increases from 30 nm to 550 nm. Therefore, the proper selection of In0.01Ga0.99N layer thickness in In0.03Ga0.97N/In0.01Ga0.99N UWG is beneficial to improve the performance of GaN-based LDs.
Fig. 9. (a) P-I curves and (b) output power at 120 mA and threshold current versus the thickness of In0.01Ga0.99N layer in In0.03Ga0.97N/In0.01Ga0.99N UWG.
4. Conclusion
In this research, the effects of the variation of Al content in p-CL, material composition and thickness of UWG are theoretically investigated in order to improve the optical and electrical properties of GaN-based LDs. It is found that increasing the Al content in p-CL is beneficial to enhance the confinement of the optical field, driving it away from the p-type side. Meanwhile, the threshold current is reduced and the output power is increased correspondingly. In addition, when In0.03Ga0.97N/In0.01Ga0.99N UWG replaces the conventional GaN and InGaN UWGs, the photoelectric characteristics of LDs are further improved. Furthermore, it is found that as the thickness of In0.01Ga0.99N layer in the In0.03Ga0.97N/In0.01Ga0.99N UWG increases from 30 nm to 550 nm, the output power enhances and then decreases, and the maximum value reaches 157.6 mw when the thickness is 400 nm, while the threshold current drops and then rises, with the lowest threshold of 23.9 mA at a thickness of 250 nm. Therefore, a proper choice of the thickness of In0.03Ga0.97N/In0.01Ga0.99N UWG will be more favorable to obtain the superior performance of LDs.
Funding
Strategic Priority Research Program of Chinese Academy of Sciences (XDB43030101); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2019115); National Key Research and Development Program of China (2018YFB0406903); National Natural Science Foundation of China (61874175, 61904172, 61974162, 62034008, 62074140, 62074142).
Acknowledgments
This work was supported by the National Key R&D Program of China (Grant No. 2018YFB0406903), the National Natural Science Foundation of China (Grant Nos. 62034008, 62074142, 62074140, 61974162, 61904172, 61874175), Beijing Nova Program (Grant No. 202093), and the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No. 2019115).
Disclosures
The authors declare no conflicts of interest.
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