In this paper, a pulsed electrically pumped GaN-based vertical-cavity surface-emitting laser (VCSEL) with one dielectric distributed Bragg reflector and one n-GaN monolithic high-index contrast grating (MHCG) mirror was demonstrated at room temperature. The reflectance of the n-GaN MHCG and cavity mode behaviors of the VCSEL with MHCG for varying n-GaN thickness, MHCG pattern diameter, and current aperture size were numerically investigated. Measured characteristics of the fabricated device showed that the lasing action started at an injection current of 10.2 mA, corresponding to a current density of about . Above threshold, the measured slope efficiency was , and the output power was 0.13 mW at 30 mA. Moreover, the measured lasing peak occurring at 403.4 nm and the longitudinal mode spacing of 5.6 nm were in good agreement with simulations. The incorporation of an n-GaN MHCG mirror not only greatly simplified the fabrication but also substantially improved the lasing characteristics in comparison to the previous work applying HCG mirrors.
© 2021 Chinese Laser Press
Vertical-cavity surface-emitting lasers (VCSELs) have been developed for over forty years and have attracted considerable attention due to many advantageous features, such as the light beam emitting from the top surface, circular and low-divergence beam, low threshold operation, compact size, and high output power brought by array of lasers. To date, VCSELs are considered as established light sources to be widely used in numerous applications, e.g., laser printing , laser display , optical communication [3,4], optical clock , gas sensor [6,7], three-dimensional (3D) sensing, and light detection and ranging (LiDAR) application [8–10], which operate in red to mid-infrared (MIR) wavelength bands. To have even shorter-wavelength devices, GaN-based VCSELs have quickly evolved in recent years [11–14]. Especially distributed Bragg reflectors (DBRs) for nitride-based VCSELs have been considered the most critical component to ensure proper laser operation. Different types of DBRs have been demonstrated, including epitaxial DBRs [15,16], dielectric DBRs [17,18], air-gap DBRs [19,20], and nanoporous DBRs [21,22]. We recently demonstrated a free-standing high-index contrast grating (HCG) with high reflectivity of up to 95% and wide bandwidth of 25 nm in the visible light spectrum . Furthermore, an optically pumped GaN microcavity and an electrically pumped GaN-based VCSEL with specific HCGs for emitting the transverse magnetic (TM) and transverse electric (TE) polarized light have been realized successfully [24,25]. The feature of polarization control becomes one of the advantages of VCSELs with HCGs. However, there are some technical issues for creating a highly reflective HCG mirror deposited on the GaN layer. layers deposited by spin coating , sputtering [27,28], or ultrasonic spray pyrolysis  suffer from thickness uncertainty/surface roughness, over-etching, and a nonnegligible extinction coefficient ( for a wavelength of [27–29]) in the blue-ultraviolet wavelength regime. Even when the film was prepared by atomic layer deposition (ALD), resulting in a much-reduced extinction coefficient of , the corresponding absorption coefficient was still over for a wavelength of 400 nm [30,31]. Referring to the development of mid-infrared VCSELs with integrally formed suspended HCG mirrors [32,33] and near-infrared VCSELs with GaAs-based monolithic HCG (MHCG) [34,35], GaN MHCG mirrors should be able to integrate with GaN-based VCSELs because the free-carrier absorption coefficient of n-GaN is only in the magnitude of .
As a result, we proposed and designed GaN-based VCSELs with GaN MHCG mirrors directly constructed by electron-beam lithography and dry etching. It was found that previous works about InP-based mid-infrared VCSELs with HCG mirrors only showed the reflection spectra of the HCG structure [37,38]. For GaAs-based VCSELs, several simulation works about GaAs HCG mirrors have been published [32,39,40], and the numerical and experimental results have elucidated the impact of HCG parameters on resonant wavelength and threshold current of VCSELs with air-suspended HCGs . As for the vertical microcavities directly integrated with an MHCG and a DBR and/or sandwiched by two MHCGs, the impact of MHCG parameters on the quality factor and resonant wavelength has been studied . However, a more comprehensive study on influences of geometric parameters such as duty cycle, height of the MHCG, cavity thickness, and aperture size on the cavity resonance and threshold material gain of GaN-based VCSELs has not yet been clearly disclosed.
In this paper, we will simulate the reflectance spectra of an HCG mirror made by n-doped GaN (n-GaN) for varying HCG geometric parameters including period, duty cycle, and height, and we further investigate the effects of HCG parameters and n-GaN thickness on cavity mode behaviors for a periodic unit cell of VCSELs combining an MHCG through the two-dimensional (2D) finite element method (FEM). Subsequently a 2D cross-sectional VCSEL structure with a finite number of MHCG will be built to investigate the effects of aperture size and MHCG pattern size on the lasing mode properties. Finally, the fabrication and measurement of the first ever reported current-injected GaN-based VCSELs integrated with MHCG mirrors will be demonstrated and analyzed.
2. OPTICAL SIMULATION
In the following optical simulations, we used the finite element frequency domain technique by using COMSOL Multiphysics. The schematic of a 3D rectangular HCG structure placed on the n-GaN layer in shown in Fig. 1(a). The grating’s period, width, and height are labelled as , w and h respectively. The period Λ of 375 nm was chosen to yield a peak reflectivity from the HCG at a wavelength of 403 nm to match the photoluminescence (PL) peak from the InGaN quantum wells. The cyan arrows indicate the electric-field directions of TE- and TM-polarized light. Moreover, the color distribution indicates the electric field intensity under the TE-polarized light excited at the bottom face of the n-GaN layer. The white arrowheads illustrate the electrical energy flowing back to the n-GaN layer for favorable design of highly reflective grating.
Figures 1(b) and 1(c) are the TE reflectance maps (TM reflectance contours) of HCG mirrors made by and n-GaN, respectively, for a period Λ of 375 nm and an incident wavelength at 403 nm. Here, two normalized geometry parameters are defined as and . For comparison of two kinds of HCGs made by the ALD-deposited layer and as-grown n-GaN, the refractive indices of and n-GaN at a wavelength of 403 nm used in the simulations are 2.671  and 2.531 , respectively. The magenta zones inscribed in Figs. 1(b) and 1(c) signify the evaluated TE-polarized reflectance greater than 0.995. These two reflectance maps are very similar; however, the larger magenta zone of the HCG mirror made by n-GaN implies that the fabrication window of HCG can be larger with parameters (Fw, Fh) (30%–42%, 25.5%–28.5%). The TE reflectance spectra of the n-GaN MHCG mirror for parameters (Fw, Fh) versus wavelength are shown in Figs. 1(d) and 1(e). Clearly, the simulated results denote that the central wavelength of TE-polarized reflectance is very close to 403 nm. It can be found that the calculated reflectance is strongly dependent on the Fh but weakly dependent on the Fw. The period- and duty-cycle-dependent reflectance map of n-GaN MHCG is also shown in Fig. 1(f). In order to obtain a high reflectivity above 99.5%, a period within and a duty cycle of are required. It is worth noting that the effect of the HCG’s sidewall angle on the reflectivity was also investigated [see Figs. 5(a) and 5(b) in Appendix A for the effect of sidewall angle on the reflectivity]. In the case of , the highest reflectivity has no significant drop for the trapezoid-shaped HCGs with 15° of tilted angle.
Then, a periodic unit cell model was considered to calculate the cavity mode characteristics of a GaN-based VCSEL structure with 10 pairs of InGaN/GaN multiple quantum wells (MQWs). The simple sketch of a periodic VCSEL unit cell is shown in the inset of Fig. 6(a) (Appendix B), and the detailed VCSEL layer structure is shown in Fig. 3(a). The material gain spectrum was described by a Gaussian function with a maximum at 403 nm and a standard deviation of 10 nm. The absorption coefficients of the p-doped electron blocking layer (p-EBL), p-doped GaN (p-GaN), and indium-tin-oxide (ITO) layer were assumed to be 50, 100, and , respectively. In our calculation, the bottom dielectric DBR was considered as a lossless medium. The calculations of cavity mode wavelength and threshold gain were performed by 2D FEM eigenvalue analysis. We used the stationary iterative method and tuned the peak of the material gain spectrum to solve the eigenmode problem for searching a minimum threshold gain when the modal loss is compensated for by the material gain. The effect of cavity thickness and Fano resonance has been detailed in Appendix B. Figures 2(a) and 2(b) summarize the calculated threshold gain mapping of a VCSEL unit cell with an MHCG mirror and a HCG mirror for varying HCG parameters (Fw and Fh). Characterized threshold gains are compartmentalized by using different color blocks, and white contours indicate associated cavity mode wavelengths. Evidently, there is an ellipse-like zone having a relatively lower threshold gain of illustrated by a green dashed contour that falls within the range of and . The minimum threshold gains of a VCSEL unit cell with two kinds of HCGs without considering the light scattering loss that results from the light leaking out of the cavity are at ( and ) and at ( and ). From Fig. 2(b), we can see that the threshold gains for the case of HCG are higher than those of VCSELs with GaN MHCGs, and the low-threshold gain area is smaller. In addition, the impact of sidewall angle on the threshold gain has also elaborated. The minimum threshold will be increased by 1.14% and 2.02% for sidewall angles of 10° and 15°, respectively. Moreover, the suitable HCG parameters for a low-threshold VCSEL laser will shift to a slightly smaller Fw and Fh as compared with aforementioned result (see Fig. 8 in Appendix C for the effect of sidewall angle on the threshold).
To account for the light scattering effect on the threshold gain from the aperture size and HCG pattern diameter, a 2D cross-sectional VCSEL structure combining a GaN MHCG mirror with , , a period of 375 nm, and a 3155 nm thick n-GaN was simulated, and the results are shown in Fig. 2(c). Here, MQWs located outside the aperture have the absorption coefficient of . The blue symbols show the calculated threshold gain when the HCG pattern diameter is the same as that of the aperture. By contrast, the red symbols represent the threshold gain as a function of the HCG pattern size that is larger than the aperture size for a fixed aperture diameter of 9 μm. The top horizontal axis variable means the diameter of the HCG pattern is 0 to 16 μm larger than that of the aperture. As a consequence, the lateral scattering loss induced by the higher-order diffractions and the metal absorption loss induced by the aperture and discontinuous interfaces of the underlying DBRs play critical roles in the modal loss. It is noticed that MHCG induces undesirable first-order diffraction, and the aperture also induces some diffractions. Due to the fact that standing resonant light has nonzero lateral wave vector components that are not totally reflected by DBR, part of the diffracted light is absorbed by metal below the DBR, and the remaining part reflected by DBR laterally leaks out of the cavity, which can be nicely seen in Figs. 2(d)–2(g). As a result, the calculated threshold gain is increased by at least a factor of 2 from that of Fig. 2(a) when considering the light diffraction.
The modal loss can be divided into vertical mirror loss, vertical scattering loss (light leaks from flat n-GaN), horizontal scattering loss (light will be absorbed by lossy media), and metal absorption loss. Typically, the vertical mirror loss is inversely proportional to the aperture size. However, the lateral diffractive scattering field is guided by DBR/metal (Au) and air due to the total internal reflection effect, and the propagation paths of lateral diffractive scattering fields will be modulated by the aperture size for a fixed mesa. So the behavior of horizontal scattering loss will be an oscillating decreasing phenomenon as the aperture size increases (see Fig. 9 in Appendix D for the oscillating phenomenon). Therefore, the combined effect causes an inflection point in the blue fitting curve as plotted in Fig. 2(c), which results in a local minimum threshold gain when aperture size is within the range of 8 to 9 μm.
On the other hand, when the HCG pattern diameter is larger than that of the aperture, the threshold gain will slightly increase. This is due to the fact that the laterally extended HCG would excite more diffractive scattering losses. Correspondingly, the normalized half-symmetric mode intensities of a VCSEL with a 9 μm aperture for four different HCG pattern sizes are shown in Figs. 2(d)–2(g). The color range of the cavity modes is highlighted to perceive lateral diffractive waves. Then, in the case of an aperture diameter of 9 μm, the size difference between HCG and aperture is preferred in a range of 11 to 12 μm. Since the accurate alignment between the HCG pattern and aperture is rather difficult, an aperture diameter of 9 μm and a 20 μm wide HCG pattern are chosen as a candidate for the GaN-based VCSEL with a monolithic HCG mirror.
3. DEVICE FABRICATION
Figure 3(a) illustrates a 3D schematic drawing of the fabricated current-injected VCSEL with a bottom dielectric DBR and a top HCG mirror. The VCSEL was grown on a sapphire substrate and consisted of a 2 μm thick undoped bulk GaN, a 5 μm thick n-GaN, 10 pairs of InGaN/GaN MQWs, an 8.8 nm thick p-electron blocking layer, and a 140 nm thick p-GaN. The wafer is actually the same as what we made for VCSELs with a HCG mirror . After that, a 30 nm thick current aperture with a diameter of 9 μm was deposited on the p-GaN by ALD. Subsequently, a 30 nm ITO layer and a 12-pair DBR were deposited by sputtering and electron beam evaporation, respectively. After the wafer was upside-down bonded to another Si substrate by gold-gold thermos-compression bonding, the sapphire substrate was removed by laser liftoff, and the undoped GaN and n-GaN were polished to a final thickness of roughly .
Finally, the HCG mirror was directly fabricated in the top of the n-GaN layer through electron beam lithography to define the 60 nm thick hydrogen silsesquioxane (HSQ) dry etch mask, and reactive ion etching to transfer the pattern into the n-GaN, followed by HSQ mask removal by a buffered oxide etch. It is noted that the grating height and thickness of the n-GaN are crucially important parameters for VCSELs with MHCG mirrors. The high-resolution transmission electron microscopy (TEM) images of the MHCG and VCSEL structure are shown in Figs. 3(b) and 3(d).
Slightly trapezoid-like n-GaN gratings were observed and had a measured top (bottom) grating bar width of 127.1 (169.4) nm, height of 98.8 nm, and period of 375.6 nm (optimal HCG parameters for a low-threshold VCSEL are a grating bar width of , a height of , and a period of according to simulations). The top and bottom widths of the grating correspond to duty cycles of 33.8% and 45.1%. The average duty cycle is still less than 40%, which is located in the high-reflectivity zone according to the simulations. Moreover, the sidewall angle of HCG was estimated at around 12°, and the simulation forecasted reflection of HCG with trapezoid shape can still be higher than 0.995 [see Fig. 5(c) in Appendix A]. The thickness measured from the ITO layer to the top of the HCG is near 3.58 μm. Furthermore, the optical microscope (OM) image of a VCSEL with an n-GaN HCG mirror is shown in Fig. 3(c). The estimated diameters of current aperture and HCG pattern are approximately 9.3 μm and 20 μm.
4. OPTOELECTRONIC CHARACTERISTICS
The light output power-current-voltage (L-I-V) curves and emission spectra measured at room temperature for the VCSEL with a monolithic HCG mirror under pulsed condition are shown in Fig. 4. The lasing was observed above a current of 10.2 mA, corresponding to a threshold current density of about . The lasing threshold was reduced significantly compared to for the VCSEL with a HCG mirror . Since we used the same epitaxial wafer to make these two kinds of VCSELs, the benefits of the GaN VCSEL with MHCG are obvious. The measured slope efficiency was about , and the output power at 30 mA was 0.13 mW.
The current-dependent electroluminescence spectra show that a lasing peak occurs at 403.4 nm, and two longitudinal modes below the threshold condition are observed with a mode spacing of near 5.6 nm. There is a small difference in the lasing wavelength and mode spacing between experiment and simulation, which could be due to a small uncertainty in the refractive index and thickness of n-GaN. A theoretical paper gave a comparison of the energy-momentum dispersions for vertical microcavities with double DBRs and HCG-DBR configurations . The dispersion of a microcavity with HCG-DBR is steeper than that of double DBRs, which means that if the lateral component of the wave vector exists in the mode, such mode suffers stronger light leakage. We supposed that our VCSEL with MHCG facilitates single-mode operation due to this special cavity dispersion. The near field above the threshold in the inset of Fig. 4(b) shows a strong single lobe at the center of the current aperture.
Moreover, the inset plotted in Fig. 4(b) is the measured polarization curve of the emission beam overlaid on the top-view SEM image of the HCG. It demonstrates that the laser has its electric-field polarized parallel to the n-GaN grating bars, i.e., TE polarized, with a degree of polarization of about 90%.
In conclusion, we have calculated the reflectance of HCG mirrors made by n-GaN and further investigated the threshold gain of a VCSEL with an n-GaN MHCG by FEM. Meanwhile, a 2D cross-sectional VCSEL with a finite extension of the MHCG was constructed to analyze the light scattering effect on threshold gains of VCSELs. The simulations revealed that the scattering loss accounted for a large part of modal loss. We then fabricated current injected VCSELs with a dielectric DBR on one side and an n-GaN MHCG mirror on the other. The threshold current of these devices was greatly reduced compared to our previous HCG VCSELs with an HCG in , which is believed to be due to the significantly lower absorption coefficient and better material quality of MHCG. The lasing wavelength and mode spacing satisfactorily match those predicted by the numerical calculations.
APPENDIX A: REFLECTANCE FOR TRAPEZOIDAL n-GaN MHCG
The schematic of periodic trapezoidal n-GaN MHCG is shown in the inset of Fig. 5(c). The effect of sidewall angle () on reflectance of trapezoidal MHCG has been investigated. Figures 5(a) and 5(b) are the simulated reflectance maps for and , respectively. The magenta zones depicted in Figs. 5(a) and 5(b) represent the evaluated TE-polarized reflectance greater than 0.995. As a consequence, if the duty cycle (Fw) and height (Fh) are located within the range of 30% to 40% and 26% to 27%, the highest reflectance of MHCG would be independent of the sidewall angle when the angle is less than 20°. Besides, we have also numerically estimated the reflectance of realistic MHCG parameters (, , and ) measured from TEM image as shown in Fig. 3(b). The angle-dependent reflectance spectra show the trapezoidal HCG can still be used as a high-reflectivity mirror.
APPENDIX B: THRESHOLD GAINS, OPTICAL CONFINEMENT, AND MODE PROFILE OF A GaN-BASED VCSEL UNIT CELL WITH A RECTANGULAR n-GaN MHCG
The simulated resonance wavelength and threshold material gain for different longitudinal cavity modes as a function of n-GaN thickness for a VCSEL with a bottom dielectric DBR and a top n-GaN MHCG mirror are displayed in Figs. 6(a) and 6(b). The n-GaN thickness does not include the height of the MHCG. The MHCG’s parameters were fixed at , , and . The gray dotted line in Fig. 6(a) denotes the targeted PL peak wavelength of 403 nm. Three resonant cavity modes near 403 nm are labelled by #1, #2, and #3. These three modes belong to different longitudinal modes. The periodic n-GaN thickness is approximately 80 nm to meet the target wavelength for different longitudinal modes, and the calculated longitudinal mode spacings for a 3155 nm thick n-GaN were 6.18 nm and 5.71 nm between #1/#2 and #2/#3, respectively. The simulated cavity mode profiles with resonant wavelength of 403 nm for n-GaN layer thicknesses of 3075, 3155, and 3235 nm are shown in Figs. 6(c)–6(e). The calculated threshold gains were 2040.8, 2009.7, and . Typically, the mode with the lowest threshold gain will dominate the lasing process. Therefore, mode #2 shall be the lasing mode when the n-GaN thickness is around 3155 nm. Variation in the n-GaN thickness away from 3155 nm will further increase the threshold gain. On the other hand, it can be seen that the resonant mode profiles appear with imperfect planar wavefronts due to the diffraction effect. The calculated optical confinements of MQW and ITO layer for different n-GaN thicknesses were also evaluated and shown in Figs. 7(a) and 7(b). Furthermore, if the n-GaN thickness is not chosen appropriately, the cavity mode can suffer from a strong Fano resonance effect where the diffraction spikes [see Figs. 7(c), 7(d), and 7(e)] induced by the periodic grating would vigorously increase the threshold material gain, caused by an increased absorption loss inside the ITO layer [see Fig. 7(b)].
Figures 7(a) and 7(b) show the calculated optical confinement factors of a VCSEL unit cell with a rectangular MHCG for and . We can see that there is a significant decrease and increase in QW and ITO confinement factors at certain n-GaN thickness, which is due to the cavity mode switched by the Fano resonance. In addition, Figs. 7(c)–7(e) show the mode profiles (#2) of a VCSEL unit cell for three different thicknesses of n-GaN layers. Selected thicknesses are corresponding to the Fano resonant peaks appearing in Figs. 7(a) and 7(b). Obviously, the hot spots of these modes significantly alter the optical confinements.
APPENDIX C: THRESHOLD GAIN OF A GaN-BASED VCSEL UNIT CELL WITH A TRAPEZOIDAL n-GaN MHCG
Figure 8 shows the Fw- and Fh-dependent threshold gains of a periodic VCSEL unit cell with monolithic n-GaN MHCG and 3155 nm thick n-GaN layer. Green and white contours indicate the threshold gain and cavity wavelength. For comparison, we found that the minimum threshold gain for a trapezoidal MHCG will increase slightly with the increasing sidewall angle. For sidewall angles of 10° and 15°, there are 1.14% and 2.02% increase in minimum threshold gain compared with the result of Fig. 2(a). Moreover, the duty cycle Fw for minimum threshold gain would shift to a smaller one for a larger sidewall angle, and the height of MHCG Fh would also slightly dwindle.
APPENDIX D: OPTICAL CHARACTERISTICS OF A 2D CROSS-SECTIONAL GaN-BASED VCSEL WITH A FINITE MHCG
Figure 9 shows the optical characteristics of a 2D cross-sectional VCSEL with a finite period of MHCG. The MQW confinement factor changes resonantly with increase in aperture size; however, there is a turning point when the aperture size is close to 12 μm. Meanwhile, the MQW absorption loss will slightly increase. In addition, the free-carrier absorption from GaN-based material seems to be independent of the aperture size, and the behaviors of absorption losses for ITO and metal look like an oscillation function with the average of the losses of approximately and , respectively. Based on the relation between the optical threshold gain and modal loss, the threshold gain exhibits an oscillatory-decreasing feature with the increase of the aperture size if the vertical mirror and scattering losses are neglected.
European Research Council (865622); Swedish Research Council (2017-04440, 2018-00295); Ministry of Science and Technology, Taiwan (MOST 109-2627-M-008-001, MOST 110-2218-E-A49-012-MBK, MOST 110-2221-E-A49-058-MY3).
The authors thank Lextar Electronics Corp., in Taiwan, Nano Facility Center, Center for Nano Science and Technology in National Yang Ming Chiao Tung University for their technical support. The authors also thank Marcus Rommel at Chalmers University of Technology for input to the process development of the high-contrast gratings.
The authors declare no conflicts of interest.
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