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Abstract
We have theoretically designed a double-lattice photonic crystal surface-emitting laser (PCSEL) based on triangular and circular holes. In the design, porous-GaN which has the properties of lower refractive index and high quality stress-free homo-epitaxy with GaN, was first proposed to be the cladding layer for GaN-PCSEL. The finite difference-time domain (FDTD), the plane wave expansion (PWE), and the rigorous coupled-wave analysis (RCWA) method were employed in the investigation. Our simulations achieved a radiation constant of up to 50 cm-1 and a slope efficiency of more than 1 W/A while maintaining a low threshold gain. We conducted a systematic study on the effects of the filling factor, etching depth, and holes shift, on the performance of the PCSEL. The findings indicate that increasing the filling factor improves the radiation constant and slope efficiency. Asymmetric hole patterns and varying etching depths have a similar effect. The introduction of asymmetric patterns and a double lattice in the photonic crystal breaks the symmetry of electric fields in the plane, while different etching depths of the two holes break the symmetry in the vertical direction. Additionally, altering the shift of the double lattice modifies the optical feedback in the resonators, resulting in variations of cavity loss and confinement factor.
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1. Introduction
Photonic crystal surface-emitting lasers (PCSELs) have garnered considerable attention in recent years due to their outstanding characteristics [1–6], including single-mode operation, low divergence angle, low line-width, and high power. As a result, PCSELs have found applications in a wide range of fields such as high-density optical storage, optical sensing, optical detection and ranging, and laser solid-state lighting [7,8].
GaN-based PCSELs, with their unique advantages in visible light communication, underwater communication, and material processing, have been the focus of increasing research interest [8–10]. The development of GaN-PCSELs began with the first report of an electrically pumped 406.5 nm lasing from Susumu Noda’s Group in Kyoto University in 2008 [11], followed by subsequent reports for both electric and optical pumping [2,12–14]. In 2020, McGill University in Canada reported a nanocrystalline surface emitting GaN-based laser, achieving an electrically pumped output with a threshold current density of 400 A/cm2 at a wavelength of 523 nm [15]. In 2022, Noda's research group reported a GaN-PCSEL achieving blue light output with an emission power of more than 1 W [16].
Improving slope efficiency and power output in lasers has always been vital. Most related works have been reported on PCSELs in the near-infrared band of 850-1600 nm [17–21]. In 2001, Noda's group demonstrated that changing the structure of photonic crystal (PhC) units can change the polarization mode in PCSELs [22]. In 2011, they investigated PCSELs with circle, equilateral triangle, and right-angled isosceles triangle as the photonic crystal geometry by using the coupled wave theory (CWT) and the Finite Difference-Time Domain (FDTD) method [23]. Their findings indicated that the surface-emitting beam is enhanced due to destructive interference, and asymmetric photonic crystal geometries can lead to higher power output. In 2014, K. Hirose prepared a square lattice PCSEL with right triangle photonic crystal geometry, which utilized asymmetric geometry to enhance the surface-emitting beam and achieved an output power of 1.5 W with a divergence angle of less than 0.5° [24].
The laser region in photonic crystals should have sufficient size to achieve high light amplification gain. However, increasing the area gradually often leads to multimode oscillation. An improved photonic crystal structure with a double lattice was proposed [25]. This structure provides an appropriate optical path difference between backward diffracted beams with a phase difference of 180°, weakening the in-plane optical limitation and flattening the light field distribution, thus increasing the luminous area. The flat light distribution causes electromagnetic modes of light to diffuse towards the edges of the photonic crystal, suppressing higher-order modes and strengthening the stability of single-mode operation [26].
In 2017, Noda's group designed a double lattice PCSEL based on double isosceles right triangle holes [27] with an oscillation wavelength of 940 nm. The device, composed of an AlGaAs/InGaAs material system, achieved a transmission area of 300 × 300 µm2, an output power of over 5 W, a narrow beam divergence of less than 1°, and a single-lobed FFP (far field pattern) under 10 A pulse operation. Subsequent experiments showed that the slope efficiency of the double lattice PCSEL was significantly increased by approximately 25 times compared to the single lattice PCSEL, attributed to the effect of the asymmetric electric field [28]. The highest experimentally demonstrated slope efficiency at around 940 nm is approximately 0.4 W/A [29]. Because roughly half of the laser light emitted toward and absorbed by the backside electrode, using a distributed Bragg reflector (DBR) as a rear reflector effectively addresses this issue [30]. Moreover, introducing asymmetry in the horizontal and vertical directions can further enhance the surface radiation effect of photonic crystals.
In 2019 and 2021, Noda's group proposed double crystal lattice PCSELs with combined elliptical and circular holes [25,26]. The design utilized an asymmetric double lattice to enhance the surface radiation effect of photonic crystals and improve in-plane optical feedback, significantly increasing laser output power. Different etching depths of the air holes effectively suppressed multimode oscillation. The device achieved a peak power of 10 W, a wide-angle beam divergence of only 0.1° at a wavelength of 940 nm, and an improved slope efficiency from 0.4 to 0.8 W/A through a DBR. Theoretical studies have also proposed a formula for slope efficiency, suggesting a theoretical upper limit. Calculations based on this formula indicate that PCSELs in the blue light band around 450 nm often have a greater slope efficiency than PCSELs at 940 nm. In 2022, Noda’s group reported a GaN-PCSEL based on an asymmetrical double lattice structure, successfully achieving blue light output with an emission power of more than 1 W [16].
In this work, we introduce a novel GaN-based photonic crystal surface emitting laser. This innovative design incorporates a low refractive index porous-GaN cladding layer and combines a RIT-C double-lattice PhC structure composed of right-angled isosceles triangle (RIT) and circle (C) elements, resulting in significantly higher slope efficiency during light emission. Traditionally, GaN-PCSELs bury the photonic crystal holes in the GaN near the active layer to improve the optical field confinement. However, this approach typically results in a limited confinement factor of about 3% [11,31]. This is because air holes cause a significant refractive index difference between the upper and lower claddings. Our design is based on porous GaN technology and enables the creation of a cladding layer with a significantly lower refractive index. It replaces the conventional AlGaN layer, which could not achieve such a low refractive index due to aluminum composition constraints, and consequently breaks free from the limitations of stringent PhC positioning demands. We design the PhC onto the GaN surface, and even in the shallow etching condition, without damaging the active region, it can achieve a high confinement factor for the optical field in both the PhC layer and the active layer simultaneously.
The RIT-C double lattice photonic crystal structure was initially proposed. The asymmetric geometry of the RIT PhC usually enhances beam emission on the surface, resulting in a higher radiation constant. Simulations using the plane wave expansion (PWE) method were conducted to study the band structure of the double-lattice photonic crystals and determine the appropriate lattice constant. FDTD simulations were performed to obtain the Q factor, confinement factor, and radiation loss of the proposed epitaxial structure. Our results demonstrate that optimizing the spatial distribution, introducing different depths of the air holes, and varying the shift of the holes can further improve laser performance, which is consistent with previous reports [28,32,33].
2. Design and simulation
Figure 1(a) illustrates the schematic diagram of the proposed PCSEL. It incorporates a unique RIT-C double-lattice PhC layer, which introduces the horizontal and vertical asymmetry. The PhC geometry combines right-angled isosceles triangle (RIT) and circle (C) elements. RIT hole PhC and C hole PhC are both square lattice with the same lattice constant a. They are etched to different depths, as depicted in Fig. 1(c). The layer thickness is d. The RIT holes have an etching depth of d1, while the C holes showcase a depth of d2. Fig. 1(b) shows other essential parameters of the double-lattice GaN PhC layer, including RIT hole side length l, C hole radius r, and the shift Δd between RIT and C hole.
Fig. 1. (a) The 3-D schematic illustration of our designed PCSEL. (b) the top view of the double-lattice PhC. (c) the side view of the double-lattice PhC.
The laser structure, from top to bottom, consists of the following layers: the top square double-lattice PhC layer which formed by p-GaN etching, p-GaN layer, AlGaN barrier layer, multi-quantum wells (MQWs) layer, n-GaN layer, porous-GaN cladding layer, and GaN substrate. The PhC layer incorporates a combination of etched air holes consisting of RIT and circular holes and its average refractive index nav, can be calculated by Eq. (1) [34].
where na and nb are refractive indices of air and background material, respectively. FF is the filling factors of double-lattice PhC and is given by Eq. (2) [34], where FF1 and FF2 are the filling factors of different single-lattice PhC. The MQWs layer contains 6 pairs of quantum wells with InGaN of 2.5 nm thickness and a GaN barrier of 12 nm thickness. For specific parameters please refer to Table 1.
Table 1. Structural parameters of the proposed GaN-PCSEL
For the electrical pumping of the design, the p-contact is on top-GaN surface with metallic electrodes on the side of PhC region and a thin ITO layer extending onto the whole PhC area. The n-contact is on the backside of n-GaN. Meanwhile, different shapes and positions of p,n-contacts can be defined to realize relatively high carrier injection efficiency in the active zone that facing under the PhC. It is also possible to optimize the p,n-GaN doping concentration and resistance in order to meet the challenge of low hole mobility of p-GaN. Introducing ITO conductive layer onto the PhC region is an effective effort to solve the problem of efficient carrier injection in the active region under PhC. ITO is transparency and has little impact on emitted laser. It has been successfully incorporated into the PCSELs with buried holes [35,36] and surface holes [34,37]. The porous-GaN is produced by heavy doped n + -GaN, it has similar or higher conductivity than n-GaN [38], thus will not degrade the carrier transportation.
The preparation technology for porous GaN with a certain thickness in GaN-based systems is well-established. Based on the reported results [38–41], nanoporous GaN layer could be controlled with certain porosity and certain thickness overall. By controlling the doping and electrochemical etching bias, it is able to control the uniformly distributed nanopore size from several to tens nanometer [38], which is far smaller than the lasing wavelength. Therefore, it could be treated as a material with a spatially uniform refractive index and has been widely used for GaN-based vertical-cavity surface-emitting lasers [39–41]. On the other hand, it gives limited influence comparing with so thick bulk nanoporous GaN region (1000 nm in our model). So in the simulation, we roughly consider it as a uniform and of a specific thickness layer. The electrochemical etch used to form nanoporous GaN is conductivity-selective, so tightly controlled porous layers requires careful design and growth of doped n-GaN layers as well as repeatable etch conditions [38]. Porous-GaN can possesses a refractive index of 1.7 or even lower, depending on the porosity [38,39,42,43]. The lower refractive index of porous-GaN is advantageous in more effectively confining the light field within the MQWs and PhC layer. The top air cladding and the bottom porous-GaN cladding allows the optical field to be well confined within the active region and the photonic crystal layer simultaneously.
Here, we employed the PWE method to obtain the photonic crystal cavity band diagram for TE mode. We used approximate method to calculate the multilayer structure which described as follows [7,44,45]: The 3D hetero-structure structure can be equivalent to infinite PhCs layer with effective refractive index. We define the effective dielectric constant of material as εb, and hole as εa, also define the dielectric constant of material as εmat and hole as εair. The effective refractive index of the entire device neff was first estimated by using RCWA method. Then, calculated out the effective dielectric constant εa and εb by Eq. (3) and Eq. (4),
The band diagram reveals the relationship between the normalized frequency (vertical axis) and the wave vector (horizontal axis) of the PhC modes. Figure 2 illustrates the band diagram, where we observe a slow-mode light in the center of the first Brillouin zone. The slow-mode light corresponds to a region of reduced frequency in the band diagram, indicating a slower propagation speed than other modes. Group velocity is given by Eq. (5).
where ω is the normalized frequency, and k is the wave vector. Figure 2 shows that the band diagram exhibits regions with nearly zero slopes, indicating that the group velocity in those regions can be considered zero according to Eq. (5). It is important to note that areas of high symmetry in the PhC facilitate the formation of standing wave oscillations. This phenomenon occurs due to the feedback provided by Bragg diffraction, which enhances the optical gain.For a two-dimensional PhC, the wave vector components parallel to the interface are conserved, meaning they remain constant throughout the PhC structure. Additionally, the dispersion relation of the surrounding air, which plays a crucial role in the behavior of light within the PhC, can be described by Eq. (6).
When k⊥is equal to 0, we can get Eq. (7).
Indeed, based on the band diagram, an inverted conical surface can be depicted with the Γ point as the vertex. This conical surface is commonly called the “light cone,” as illustrated by the shadowed region in Fig. 2. Below the light cone, the light exhibits a large divergence angle. However, in the shadowed area above the light cone, radiation in the normal direction can be generated from the Γ point. This phenomenon enables the achievement of a high-quality factor by utilizing bound states in the continuous domain.
The relationship between normalized frequency ω, lattice constant a, and resonant wavelength λ is given by Eq. (8).
In the simulation, to achieve a resonant wavelength of 450 nm, certain parameters were fixed: the radius (r) was set to 30 nm, the side length (l) to 80 nm, the shift (Δd) to 0.25a, and both depths (d1 and d2) to 100 nm. The grid precision was set to a/64. The lattice constant (a) was then varied from 182 to 192 nm in steps of 2 nm.
The increase in lattice constant leads to an increase in the effective dielectric constant, decreasing the normalized frequency. Based on the simulation results, the lattice constant of 186 nm corresponds to the closest resonant wavelength to the target of 450.4 nm.
Parameters, including radiation constant, threshold gain, and slope efficiency, are usually used to measure the output performance of the laser. The radiation constant is given by Eq. (9).
where a is the lattice constant, and Q⊥ is the quality factor in the vertical direction. The radiation constant, also called vertical radiation loss, plays a significant role in the output power of PCSELs, along with in-plane losses. The output power can be improved by increasing vertical radiation loss or reducing in-plane losses [46]. However, it is worth noting that in-plane losses are more susceptible to changes in device size. In particular, the in-plane losses decrease significantly as the device size increases [36]. When the size is large enough (for instance greater than 400 µm diameter), the in-plane losses can decrease to a very low value and practically be ignored [16,34].The threshold gain and the optical confinement factor in the active region are given by Eq. (10) and Eq. (11), respectively.
where α∥ is the in-plane loss, and α⊥ is the vertical radiation loss. Vm is the mode volume of the active region, and V is the mode volume of the whole structure. Low threshold gain can reduce unnecessary energy waste caused by external pumping and improve output efficiency, while high threshold gain is more likely to cause higher-order modes, disrupting the stability of the single-mode operation for PCSELs.The slope efficiency is given by Eq. (12).
3. Results
To evaluate the design, we conducted simulations using the rigorous coupled-wave analysis (RCWA) and the FDTD method. These simulations allowed us to investigate the light field distribution within the entire structure at the target resonant wavelength. The results, depicted in Fig. 3(a)(b)(c). The horizontal coordinate in Figure 3(a) corresponds to the vertical coordinate in Figure 3(b) and (c) and they all correspond exactly to the structure Figure 1(a). The results demonstrate that the fundamental mode field is confined within the layers between PhC layer and porous-GaN layer. Thus the field overlap with PhC and MQWs could be both high. We listed the confinement factors of the PhC layer Γphc and active layer Γ with different FF in Table 2. Considerable confinement factors were achieved in GaN based PCSELs.
Fig. 3. The optical field distributions throughout the entire structure at 450.4 nm resonant wavelength calculated by (a) RCWA (b) FDTD method in yz direction and (c) FDTD method xz direction.
Table 2. Confinement factors of the PhC layer and active layer in different FF
In the design, the RIT-C air holes are shaped as a combination of isosceles right triangle and circular holes, breaking the electric field's symmetry. This asymmetry could enhance the surface-emitting beam and produces higher power output [24].
One challenge commonly encountered in PCSELs is the heating effect, which can deteriorate the device's overall performance [27]. To mitigate this issue, expanding the luminous area of the laser is necessary. Fortunately, the double-lattice PhC structure can effectively address this concern by exploiting destructive interference under specific circumstances [16]. This phenomenon weakens the in-plane optical confinement, thereby enlarging the emission region.
However, it is important to note that multimode oscillation can occur when the emission region becomes sufficiently large. To overcome this, the double-lattice structure is designed to eliminate direct 180° coupling between the Bloch waves while maintaining indirect 90° coupling [25]. As a result, the light spreads throughout the cavity area, exhibiting a flattening phenomenon. This increases the difference in optical loss between the fundamental and high-order modes [16,53].
By employing the double-lattice PhC structure, we effectively address the heating effects and expand the emission region while suppressing multimode oscillation. These design considerations contribute to improving the performance of the PCSEL by manipulating the optical field distribution. We have simulated the far-field patterns in fundamental and higher-order modes, as shown in Fig. 4 (a) and Fig. 4 (b). The electromagnetic field distribution is symmetric if the unit cell is symmetric structure, causing destructive interference of the electric field at the center of the vertically diffracted beam and resulting in its annular shape [24]. Utilizing asymmetric structure weakens this interference, and from Fig. 4(a), it can be seen FFP has the shape of a single circular lobe with a narrow divergence angle, which also indicating that single-mode operation at the Γ point was achieved. As shown in Fig. 4(b), the divergence angle of higher-order modes is wider than that of fundamental mode, which means that higher-order modes distributed more in cavity edge comparing with fundamental mode, thus is more likely to leak from the edges. It ensures the stability of fundamental mode operation and reducing the possibility of higher-order mode appearing. And this issue also discussed in paper [25].
We investigated the influence of different filling factor on the output performance of the GaN-PCSEL. Firstly, we conducted simulations and compared two different devices: Sample 1, where the PhC geometry is composed of a combination of ellipse and circle, and Sample 2, where the PhC geometry is RIT-C.
To minimize in-plane optical feedback and achieve a flattened light field distribution, we set Δd = 0.25a[16]. However, due to the restriction of Δd, the size of each hole was limited. It is important to note that as the etching depth of the holes increase, the effective refractive index of the PhC layer decreases. Consequently, the light field tends to move towards the active region and downwards to the n-GaN layer. We set the etching depth to 100 nm to maintain an optimal field distribution.
In Sample 2, when the FF are 13.5% and 16.5%, the radiation constants are 21.9 cm-1 and 29.47 cm-1, the threshold gains are 61.5 cm-1 and 82.3 cm-1, and the slope efficiencies are 1.11 W/A and 1.19 W/A, respectively. In Sample 1, with the same FF values of 13.5% and 16.5%, the radiation constants are 20.3 cm-1 and 23.91 cm-1, the threshold gains are 61.3 cm-1 and 71.42 cm-1, and the slope efficiencies are 1.0 W/A and 1.1 W/A, respectively. Both Sample 1 and Sample 2 exhibit low threshold gains, indicating a low level of gain required to achieve lasing oscillation. This is largely attributed to the high quality factor resonance and high confinement factor of active region brought by porous-GaN and air claddings. However, Sample 2 with RIT-C configuration demonstrates higher radiation constants and slope efficiencies than Sample 1.
To further demonstrate the superiority of the RIT-C double-lattice, we conducted a comparative analysis of PCSELs with single-lattice PhC structures. Specifically, we examined the RIT and C configurations separately. Figures 5 (a), (b), and (c) illustrate the impact of varying the FF on the radiation constant, threshold gain, and slope efficiency. The three parameters exhibit strong similarities, as the threshold gain and slope efficiency are primarily influenced by the radiation constant, as supported by Eq. (10) and Eq. (12).
Fig. 5. Calculated (a) radiation constant, (b) threshold gain and (c) slope efficiency are a function of FF for RIT&C-shaped, RIT-shaped and C-shaped holes, respectively. Calculated (d) radiation constant, (e) threshold gain and (f) slope efficiency are a function of RIT&C-shaped hole’s etching depth ratio d1/d2. Calculated (g) radiation constant, (h) threshold gain and (i) slope efficiency are a function of RIT&C-shaped holes’ shift Δd.
For the device with a circular hole, the radiation constant, threshold gain, and slope efficiency increase gradually and maintain a relatively low level. It has shown that the radiation constant of a circular hole is minimally influenced by FF due to the protection offered by the symmetrical structure [35]. Although the device successfully achieves a low threshold gain, the low slope efficiency poses challenges for improving the output performance yet. On the other hand, the other two configurations, which break the symmetric electric field, exhibit significantly improved radiation constants. When the FF is less than 14%, the radiation constant remains relatively stable, and as the FF surpasses 14%, it gradually increases before reaching a peak value and subsequently decreases. Similar trends are observed for the threshold gain and slope efficiency. By comparing the devices, we find that the geometry of RIT-C in the double-lattice PhC structure yields a higher radiation constant, resulting in higher threshold gain and slope efficiency. This observation is precisely consistent with the expectations based on Eq. (10) and Eq. (12).
Figures 6 (a), (b), and (c) shows the calculated |E|2 distribution of the different devices at an FF of 17%. Notably, the double-lattice PhC allows for degraded coupling of light in the PhC layer compared to the single-lattice configurations, resulting in a more uniform distribution of the light field and consequently achieving a brighter and larger luminescent area.
Fig. 6. The x-y plane |E|2 distribution of PCSEL with different PhC geometry calculated by FDTD method. (a) A combination of RIT and C, (b) RIT, (c) C.
It is important to note that the structure of the devices remains unchanged in the vertical direction, causing a roughly equivalent confinement factor for the active region. Therefore, an increase in the radiation constant, as predicted by Eq. (10), inevitably leads to an increase in the threshold gain. Simultaneously, the slope efficiency also improves, as indicated by Eq. (12). To achieve optimal results, selecting appropriate parameters that strike a balance between a low threshold gain and a high slope efficiency is crucial.
To investigate the impact of asymmetry in the vertical direction, we maintained the values of r (30 nm), l (80 nm), Δd (0.25a), and d2 (100 nm) while varying d1 from 50 nm to 150 nm. This resulted in a range of d1/d2 ratios called the etching depth ratio. Figures 5 (d), (e), and (f) depict the influence of changing the etching depth ratio on the radiation constant, threshold gain, and slope efficiency, respectively. We chose the air layer above the photonic crystal to the output port, and the change in d1/d2 result in an increase in vertical radiation loss. We compared the radiation constants in + z and -z directions with different d1/d2, which indicate that d1/d2 exert more influence on the front side. The data are all based on + z direction.
The results demonstrate that introducing asymmetry in the vertical direction increases the radiation constant, consequently boosting the slope efficiency. This phenomenon can be attributed to the disruption of the symmetrical electric field in the vertical direction, which improves the system instability [22,23]. As d1/d2 increases from 0.4, the etching depth’s difference gradually diminishes, and the vertical asymmetry reduces. This results in improved system stability and a downward trend in the curve. The vertical asymmetry disappears entirely when d1/d2 is approximately 1, meaning the uniform etching depth. Consequently, the radiative constant, threshold gain, and slope efficiency decrease to their minimum values. Subsequently, with a further increase in d1/d2, the etching depth’s difference gradually enlarges, and the vertical asymmetry grows, leading to an upward trend in all the curves. Furthermore, increasing the etching depth decreases the effective refractive index in the PhC, makes the field profiles moves downward further (moves to the right in Fig. 3(a)) resulting in a decreasing of the optical confinement factor in active region, which also increase the threshold gain. This also is the reason that, when the d1/d2 ratio is 1.4, we observe a slightly higher threshold gain than the d1/d2 ratio 0.6.
We continued to investigate the effect of the shift between holes. In this scenario, we maintained r (30 nm), l (80 nm), d1 (100 nm), and d2 (100 nm), and varied Δd, while ensuring that Δd is not too small to avoid hole overlapping. Previous research indicates that when Δd is 0.25a, destructive interference occurs, weakening in-plane feedback, while Δd of 0.5a leads to constructive interference, enhancing in-plane feedback [16]. Figures 5 (g), (h), and (i) illustrate the influence of changing Δd on the output performance of PCSELs.
Our findings reveal that when Δd is less than 0.35a, there is a high radiation constant. However, as Δd exceeds 0.35a, the radiation constant experiences a rapid decline, stabilizing at around 11cm-1 for Δd over 0.43a. In practical terms, a Δd of 0.3a is more reasonable. Smaller Δd values will result in the overlapping of holes during the etching process, while a Δd of 0.3a yields a higher radiation constant than 0.25a[43].
We compared the performance of three devices with different parameters, as presented in Table 2. A trade-off exists between the threshold gain and the slope efficiency, necessitating a careful balance in the actual processing.
The data in Table 3 shows that Sample C exhibits a low threshold gain and a low slope efficiency. On the other hand, Sample A demonstrates higher slope efficiency than Sample C, at the expense of a doubled but relatively low threshold gain. Similarly, Sample B shows an improvement in slope efficiency compared to Sample C. However, this comes at the cost of a four-fold increase in threshold gain, reaching 146.06 cm-1. In this case, the sacrifice of threshold gain for slope efficiency does not yield a significant improvement. Finding a balance between the threshold gain and the slope efficiency is essential to achieve optimal performance. This involves selecting appropriate parameters for relatively high slope efficiency while maintaining a minimal threshold gain.
Table 3. Parameters and performance indicators of the three samples
4. Discussions
The following we discuss on the realizability and fabrication tolerance of the designed device.
The common method used to define so small linewidth holes is electron beam lithography (EBL). The linewidth of 20∼30 nm could be defined on PMMA mask according to the EBL technology [54], means the circular hole radius around 20 nm could be defined thus the final radius could be around 30 nm after dry etching according to our shallow hole depth of around 100 nm, based on detailed process investigation. Extreme ultraviolet (EUV) lithography can also satisfy the demanding, it is used in mass production because of very high yield [55]. Besides, multi electron beam EBL technology which can promote the EBL efficiency [54], is an alternative solution with high manufacturing volume.
The fabrication tolerance of holes proportion FF, hole’s etching depth ratio d1/d2, and holes’ shift Δd, could be represented by Fig. 5. Although they all produce apparent influence on the gain threshold, maintained at around 100 cm-1 overall. It is a small value range in PCSELs threshold gain. The low threshold gain obtained in our design is largely attributed to high confinement factor of active region brought by porous-GaN and air claddings also the high quality factor resonance. For the influence on slope efficiency, Δd has relatively significant impact. But they all have an optimized flat-top in the figure, which represent the redundant error tolerant about 5% for FF and 0.1a for Δd. Besides, from comparison, C-shaped hole PhC has higher parameter tolerance while the RIT-shaped has the most conspicuous variation impact on Q, gain threshold and slope efficiency.
The hole profile is also an important issue for our PhC structure, especially for the RIT hole. The shape of PhC will influence the Q factor of resonance and may bring variation of laser performance. It is predictable that, the fabricated structure of the designed triangle is highly likely a deformed triangle with rounded corners. However, there is report indicated that this kind of deformed triangle possesses better performance in Q-factor and gain threshold for PCSEL [56]. Furthermore, the degree of the deformation can be further controlled by designing different masks in lithography.
It should be specially mentioned that nanoporous-GaN is formed by electrochemical etching after epitaxial growth, but not in the epitaxial growth. In the real device, we grow GaN-based PCSEL structure with heavily Si-doped n-type GaN instead of nanoporous GaN. After finishing the epitaxial growth, we do electrochemical etching to make n + -GaN nanoporous, which has been widely used [39–41]. In the electrochemical etching, an anode bias voltage is applied to a highly doped n + -GaN immersed in an electrolyte, and then n + -GaN is oxidized by surface holes and dissolved in the electrolyte, forming a nanoporous layer, and the nanopore size could be precisely controlled as several nanometers, which is far smaller than the lasing wavelength. On the other hand, 200-nm-thick n-GaN waveguide layer is between MQWs and n + -GaN layer (porous-GaN in Fig. 1(a)), which could largely reduce the optical intensity distributed in the nanoporous GaN layer together with the very small refractive index of nanoporous GaN. Therefore, nanoporous GaN would not degrade the device performance.
We compared our design to other devices reported based on double lattice or blue PCSELs, which can be seen in Table 4. Apparently, this design has advantages in confinement factors and the slope efficiency. Besides, the threshold gain remains in a low value range. Although the slope efficiency and threshold is theoretical results, the outstanding confinement factors brought by porous-GaN and the optimized RIT-C double lattice with depth modulation makes highly anticipated performance to the fabricated device in the future.
Table 4. Performance indicators of this design and other reports
5. Conclusion
In this study, we aimed to enhance the output performance of GaN-PCSELs by introducing asymmetry into the PhC pattern. This disruption of the symmetrical electric field resulted in improved performance. To further enhance the radiation constant and slope efficiency, we utilized a RIT-C double-lattice PhC. Based on this, we achieved a higher radiation constant, leading to improved slope efficiency in PCSELs compared to the single-lattice PhC configuration. Moreover, we explored the impact of different etching depth ratio in the double-lattice PhC. This adjustment proved beneficial for both the radiation constant and slope efficiency. By manipulating the shift between holes, we modified the optical feedback within the cavity, further enhancing PCSEL performance. Specifically, when the shift ranged from 0.25a to 0.35a, a weakening of the optical confinement in the cavity resulted in a larger luminescent area and higher radiation constant.
However, it is important to note that improving the slope efficiency may lead to higher threshold gain, making it challenging to achieve an optimal value for both parameters simultaneously. Nonetheless, through careful parameter selection and optimization, it is possible to strike a balance and attain a relatively high slope efficiency while maintaining a small threshold.
Funding
Open Fund of State Key Laboratory of Information Photonics and Optical Communications (BUPT) (IPOC2021B03); Open Fund of State Key Laboratory of Advanced Optical Communication Systems and Networks (2023GZKF018); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX22_0945).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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