We analyzed the optimal waveguide structure of two types of InGaN-based photonic crystal surface-emitting lasers (PCSELs) to suppress the coupling with leaky modes via mode simulations. To minimize the threshold material gain (gth), we calculated the confinement factor and quality factor of PCSELs with varying waveguide layer thicknesses in the separate confinement heterostructure (SCH) layer. The optical mode intensity profile revealed the coupling between the fundamental mode of SCH and parasitic leaky modes in the cladding layer or substrate as the primary root cause of the low-quality factor and high threshold gain of PCSELs. The asymmetric nature of the SCH structure yielded the optimal waveguide structure to be dependent on the position of the air holes. With a proper waveguide thickness and air hole depth, the optimized threshold modal gain of PCSELs with the n-side air holes can be less than 30 cm−1.

In recent years, the rapid development of augmented reality technology has led to a demand for light sources with a higher power density, a lower divergence angle, a reduced weight, and an improved overall efficiency.1–3 Both micro-light-emitting diode (LED) and micro-organic light-emitting-diode (OLED) displays have encountered issues such as optical crosstalk and inadequate illuminance while the pixel density further enhances.4–11 Although these challenges might be mitigated with a proper micro-lens or a collimating metasurface design,12–14 replacing the light source with photonic crystal surface-emitting lasers (PCSELs) is also a strong alternative due to its coherent emission and narrow divergence.15–17 In PCSELs, the band edge modes of photonic crystals are coupled with the fundamental mode of the separate confinement heterostructure (SCH), so the surface-emitting lasing could be leveraged with a large-area gain medium. Therefore, PCSELs could offer a much higher power intensity than traditional micro-LED and micro-OLED displays, which is critical for applications in outdoor environments.

The air holes were placed in the p-side of the SCH laser for long-wavelength GaAs-based PCSELs. Device improvement strategies included dual-lattice photonic crystals, low-symmetry air holes, underlying reflectors, and others.18–24 However, unlike GaAs-based PCSELs, the optimal structure of GaN-based PCSELs remains inconclusive. In 2008, Matsubara et al. introduced the first PCSELs operating in the blue–violet wavelength range using InGaN/GaN materials, where the air holes are replaced with the n-side of the SCH.25 Later, Kawashima et al. placed the air holes in the p-side of the SCH and demonstrated an improved output power.26 Wu et al. chose to etch through the SCH for a stronger light–matter interaction.24 However, such strategies imposed additional barriers to electrical pumping. Recently, Liu et al. proposed an external TiO2 photonic crystal slab on top of the GaN-based membrane PCSEL with optical simulations.27 Emoto et al. also demonstrated a Watt-class blue PCSEL with air holes back to the n-side of the SCH. The improvement is attributed to multiple root causes, including changes in hole patterns and advancements in fabrication technology.28 Since the final performance is strongly influenced by different groups’ III-nitride growth and processing capabilities, judging the superiority among different PCSEL designs from published results could be biased or misleading. Therefore, an unbiased comparison with theoretical simulations is beneficial in the current stage of GaN-based PCSEL development.

In this study, we conducted a comprehensive PCSEL waveguide simulation with air holes on either the n-side or p-side of the SCH. We revealed an unexpected root cause for the low-quality factor (Q-factor) in PCSELs due to the coupling to the parasitic leaky modes. The strategies of leaky mode suppression and the root of asymmetry of optimal design due to the different positions of air holes were also discussed.

A three-dimensional optical mode simulation was conducted by the plane wave expansion method and finite element method through COMSOL Multiphysics to acquire the fundamental mode profile and then calculate the resulted confinement factor of quantum wells (Γ), Q-factor, and threshold material gain (gth) for the active region. Figure 1 presents two types of PCSELs with a photonic crystal slab buried in the different sides of SCH; both structures consisted of a common 30 nm indium-tin-oxide (ITO) at the top, followed by a 700 nm p-cladding layer, a p-In0.03Ga0.97N waveguide layer, a 15 nm p-Al0.2Ga0.8N electron blocking layer (EBL), two pairs of InGaN quantum well (QW) and GaN barrier, an n-In0.03Ga0.97N waveguide layer, a 700 nm n-cladding layer, and a GaN substrate. For brevity, the PCSEL with a photonic crystal slab on the p-side is named p-PCSEL and that on the n-side is named n-PCSEL. For p-PCSEL in Fig. 1(a), the p-cladding layer is GaN and the n-cladding layer is Al0.05Ga0.95N, while vice versa for n-PCSEL in Fig. 1(b). Since the air holes reduce the average refractive index significantly, the air holes were buried in the high-index GaN, while the low-index AlGaN was placed on the other side of the cladding layer to mitigate the asymmetry of the refractive index profile. The n-InGaN waveguide thickness (tn) and p-InGaN waveguide thickness (tp) are the major parameters for structure modulation. The air holes were placed in the vicinity of the waveguide/cladding layer interface while its height (th) was initially set to 200 nm. The in-plane lattice constant of the square lattice was 180 nm, and the hole radius was 36 nm for a photonic crystal band edge mode in the vicinity of 440 nm. The refractive indices and absorption coefficients within the structures can be referred to Refs. 29–31, as summarized in Table I. The absorption loss coefficients of p-layers are set to be much higher than those of n-layers because of the inevitably higher Mg doping level than the Si doping level.

FIG. 1.

Schematic of the InGaN-based PCSEL with a photonic crystal placed in the (a) p-side (p-PCSEL) and (b) n-side (n-PCSEL) of the waveguide structure. The simulated |Hz| profile of four distinct band edge modes, which were known as (c) A mode, (d) B mode, (e) C mode, and (f) D mode, was mapped along the cross section of the quantum well in the unit cell. The white dashed circle depicts the perimeter of the air hole.

FIG. 1.

Schematic of the InGaN-based PCSEL with a photonic crystal placed in the (a) p-side (p-PCSEL) and (b) n-side (n-PCSEL) of the waveguide structure. The simulated |Hz| profile of four distinct band edge modes, which were known as (c) A mode, (d) B mode, (e) C mode, and (f) D mode, was mapped along the cross section of the quantum well in the unit cell. The white dashed circle depicts the perimeter of the air hole.

Close modal
TABLE I.

Thickness, refractive index (n), and absorption coefficient (αi) of the layers of p-PCSEL/n-PCSEL at 440 nm.

LayerThickness (nm)n29,30αi (cm−1)31 
ITO 30 2.13 2000 
p-GaN/p-Al0.05Ga0.95700 2.50/2.45 75/75 
p-In0.03Ga0.9740–100 (tp2.54 25 
p-Al0.2Ga0.8N (EBL) 15 2.35 50 
Two pairs of u-GaN/InGaN 5/3.3 2.50/2.70 NA 
n-In0.03Ga0.9740–100 (tn2.54 
n-Al0.05GaN0.95/n-GaN 700 2.45/2.50 5/5 
GaN substrate 500 2.50 
LayerThickness (nm)n29,30αi (cm−1)31 
ITO 30 2.13 2000 
p-GaN/p-Al0.05Ga0.95700 2.50/2.45 75/75 
p-In0.03Ga0.9740–100 (tp2.54 25 
p-Al0.2Ga0.8N (EBL) 15 2.35 50 
Two pairs of u-GaN/InGaN 5/3.3 2.50/2.70 NA 
n-In0.03Ga0.9740–100 (tn2.54 
n-Al0.05GaN0.95/n-GaN 700 2.45/2.50 5/5 
GaN substrate 500 2.50 
Four photonic crystal band edge modes, which are also known as the A/B/C/D mode from the different photonic subband bands, were solved. The corresponding absolute z-component of the magnetic field, |Hz|, profiles in the active region within the unit cell is illustrated in Figs. 1(c)1(f). B-mode is often the primary lasing mode because of its destructive interference in the far-field and a stronger in-plane feedback, which results in the highest Q-factor among all modes.32 Therefore, we only list the simulation results of the B-mode for comparison in this study for concision. The Γ of B-mode was evaluated by
Γ=QW(Ex2+Ey2+Ez2)dvcell(Ex2+Ey2+Ez2)dv,
(1)
where Ex, Ey, and Ez signify the electric field components, and the integral volume in the numerator and denominator was taken over the quantum well region and the whole unit cell, respectively. The Q-factor can be calculated by
Q=2παa=2π(αi+α)a,
(2)
where “a” is the in-plane lattice constant of the photonic crystal and α is the sum of the vertical radiation loss (α) and the intensity-weighted internal absorption loss, ⟨αi⟩. ⟨αi⟩ is calculated with parameters from Table I by
αi=layeriΓiαi,
(3)
where Γi is the overlapping function of layer i,
Γi=layeri(Ex2+Ey2+Ez2)dvcell(Ex2+Ey2+Ez2)dv.
(4)
Finally, we can evaluate gth by
gth=αΓ.
(5)
Exemplary fundamental mode intensity profiles, with a common tn = tp = 60 nm and th = 200 nm, are depicted in Fig. 2, where Figs. 2(a) and 2(b) are for the n-PCSEL and p-PCSEL, respectively. Although the SCH structures between two PCSELs are similar, the resulted mode profiles along the z-axis are notably different. The calculated Γ for the n-PCSEL is 2.25%, while that of the p-PCSEL is only 1.52%. The low Γ of the p-PCSEL is attributed to the strong coupling to the leaky mode in the p-cladding layer, while the coupling to the substrate mode is much weaker in the n-PCSEL. The difference might be attributed to the asymmetric position of EBL within the SCH structure or the strong index difference outside the cladding layers. Since the refractive index of the air hole is 1, the volume-weighted refractive index of the photonic crystal slab (nPhC) can be evaluated by
nPhC=nGaN21FF+nair2FF,
(6)
where FF is the fill factor of the air hole. In this study, FF is 0.125, and the calculated nPhC is 2.36. Therefore, the index difference between the photonic crystal and the InGaN waveguide is 0.18, while that the between InGaN waveguide and the AlGaN cladding layer is 0.09, according to Table I. Therefore, the index profile of the photonic crystal/InGaN SCH/AlGaN cladding is highly asymmetric. In addition, the EBL, which also possesses a low refractive index of 2.35, is always located on the p-side of the MQW. Therefore, the n-InGaN/MQW/EBL formed another asymmetric index profile within the SCH. As a result, the optimal tn/tp configurations for Γ could significantly differ between the n-PCSEL and p-PCSEL because of the different combinations of two asymmetric index profiles. Therefore, we conducted a two-dimensional tn/tp parametric scan for both n-PCSEL and p-PCSEL optimization.
FIG. 2.

Simulated fundamental mode intensity profiles along the waveguide with the (a) n-PCSEL and (b) p-PCSEL with tp = tn = 60 nm and th = 200 nm. The gray-shaded region represents the position of air holes.

FIG. 2.

Simulated fundamental mode intensity profiles along the waveguide with the (a) n-PCSEL and (b) p-PCSEL with tp = tn = 60 nm and th = 200 nm. The gray-shaded region represents the position of air holes.

Close modal

Figures 3(a)3(c) map the dependence of Γ, Q-factor, and gth of p-PCSEL on tn and tp, respectively. The variation trends of Γ, Q-factor, and gth are similar. The (tn, tp) combination with a high Γ also possesses a high Q-factor, and the resulting gth is low according to Eq. (5). To investigate the root cause of trends, we selected four points, A to D, along the tn = tp contour and plotted the corresponding |Hz| profile along the z-axis as shown in Fig. 3(d). When tn = tp = 60 nm (point B), Γ saw a valley because of a significant coupling to the parasitic leaky mode in the p-cladding layer. The optimal structure occurred within the interested parameter space at tn = tp = 100 nm. However, the high-quality epitaxial growth of such a SCH design might be practically challenging since the critical thickness dislocation nucleation of a single In0.03Ga0.97N layer was estimated at around 80 nm in theoretical models.33,34

FIG. 3.

Dependence of (a) Γ, (b) Q-factor, and (c) gth on tn and tp for p-PCSEL. |Hz| profiles along the SCH with selected combinations of tn and tp are also mapped in (d). The white rectangle perimeter depicts the position of air holes.

FIG. 3.

Dependence of (a) Γ, (b) Q-factor, and (c) gth on tn and tp for p-PCSEL. |Hz| profiles along the SCH with selected combinations of tn and tp are also mapped in (d). The white rectangle perimeter depicts the position of air holes.

Close modal

Figures 4(a)4(c) map the dependence of Γ, Q-factor, and gth of n-PCSEL on tn and tp, respectively. The variation trends among Γ, Q-factor, and gth are similar to that of Fig. 3, where the (tn, tp) combination with a high Γ also possesses a high Q-factor and a low gth. Figure 4(d) also shows the plot of mode profiles of the same points along the tn = tp contour. The optimal Γ of n-PCSEL is around 2.3%, which is similar to that of p-PCSEL. However, this optimized InGaN waveguide’s total thickness is more feasible for coherent InGaN epitaxial growth. In a conventional edge-emitting laser (EEL) design, the SCH structure is optimized by maximizing the confinement factor and minimizing the internal loss by waveguide thickness modulation.31 In PCSELs, parasitic leaky modes are caused by inserting a low-index photonic crystal slab in the structure. The coupling between the SCH mode and the leaky mode is an unmet issue in the EEL design. If the SCH mode and the parasitic leaky mode can be decoupled by measures other than waveguide thickness modulation, Γ and gth would also be improved. For example, we might suppress the coupling by enhancing the physical distance between the SCH fundamental mode and the leaky mode with higher air holes.

FIG. 4.

Dependence of (a) Γ, (b) Q-factor, and (c) gth on tn and tp for n-PCSEL. |Hz| profiles along the SCH with selected combinations of tn and tp are also mapped in (d). The white rectangle perimeter depicts the position of air holes.

FIG. 4.

Dependence of (a) Γ, (b) Q-factor, and (c) gth on tn and tp for n-PCSEL. |Hz| profiles along the SCH with selected combinations of tn and tp are also mapped in (d). The white rectangle perimeter depicts the position of air holes.

Close modal

Figure 5 illustrates the influence of the air hole height (th) on the lasing parameters for both p-PCSELs and n-PCSELs. To reduce the number of free-varying parameters, we limited the SCH to be symmetric (tn = tp) in the following simulations. Figures 5(a)5(c) map the simulated Γ, Q-factor, and gth of p-PCSELs with varying th and tn, respectively, while Figs. 5(d)5(f) refer to those of n-PCSELs. Enhancing th from 100 to 300 nm improved all the interested parameters of PCSELs significantly, and the improvement saturated when th > 400 nm. For example, for n-PCSELs with tn = tp = 60 nm, Γ was enhanced from 2.25% to 2.41% after th increased from 200 to 350 nm. Simultaneously, the Q-factor was improved from 4464 to 9930, and gth was reduced from 3468 to 1456 cm−1. The improvement by 350 nm air holes is beyond all combinations of (tn, tp) in Figs. 3 and 4. The improvement was saturated with a high th because the SCH fundamental mode and the leaky modes were fully decoupled. For air holes with a diameter of 72 nm and th = 360 nm, the aspect ratio is 5, which might be a practical challenge for dry-etching and regrowth progress. Therefore, the design optimization of the InGaN-based PCSEL waveguide structure is not purely theoretical. Practical constraints in fabrication also need to be taken into account. In general, the n-PCSEL shall be the more favorable design than the p-PCSEL after comparing Fig. 5(c) with Fig. 5(f). The lowest gth in Figs. 5(c) and 5(f) converges to 850 cm−1 when tn = tp = 100 nm and th = 500 nm, but the total InGaN waveguide structure exceeds its critical thickness. Meanwhile, if a relatively low InGaN SCH thickness was chosen for the crystal quality, the required aspect ratio of air holes for p-PCSELs needs to be larger than that of n-PCSELs. For example, to reach gth < 2000 cm−1 with tn = tp = 60 nm, the required th is 400 nm for p-PCSELs and 300 nm for n-PCSELs—the discrepancy between n-PCSEL and p-PCSEL design window roots from the position of low-index p-EBL within the SCH. If the low-index photonic crystal slab is also placed on the p-side of the SCH, the fundamental mode penetrates into the n-side more, and a strong parasitic waveguide layer forms between the ITO and the photonic crystal slab. If the photonic crystal slab is placed on the opposite side instead, the index asymmetry is mitigated so that the fundamental mode is more concentrated in the SCH. As a result, a less th is required to suppress the undesired coupling between the SCH fundamental mode and the parasitic leaky mode. Therefore, we suggested that the n-PCSEL structure shall possess a wider design window for a lower threshold than the p-PCSEL. Recently, Emoto et al. fabricated an n-PCSEL with Jth ∼ 2.6 kA/cm2,28 while Holec et al. fabricated a p-PCSEL with Jth ∼ 3.89 kA/cm2.35 Considering that the process and epi-structure shall have been optimized to some degree, the lower threshold of n-PCSEL might be attributed to the naturally prevailing waveguide arrangement.

FIG. 5.

Dependence of (a) Γ, (b) Q-factor, and (c) gth on the symmetric waveguide thickness and th for p-PCSEL. (d)–(f) The corresponding results for n-PCSEL.

FIG. 5.

Dependence of (a) Γ, (b) Q-factor, and (c) gth on the symmetric waveguide thickness and th for p-PCSEL. (d)–(f) The corresponding results for n-PCSEL.

Close modal

Finally, we further investigated the effect of uneven distribution of tn and tp on the lasing parameters with a fixed total waveguide thickness (tn + tp = 120 nm) and a th of 300 nm. Figures 6(a)6(c) plot the dependence of Γ, Q-factor, and gth on tp, respectively. The Γ of n-PCSELs is generally higher due to the mitigated index profile asymmetry as aforementioned. Maximum Γ occurred at tp = 50–60 nm due to the alignment of QWs to the peak of mode intensity. A simultaneous thinner tp and a thicker tn shift the anti-guiding p-EBL layer farther from the center of SCH, so the Q-factor is enhanced due to the suppressed optical mode penetration into the lossy p-layers. The Q-factor enhancement is also more significant in n-PCSELs because of the lower refractive index in the p-cladding layer. The resulting gth of n-PCSELs can be further improved by uneven waveguide layer thicknesses, while the improvement in p-PCSELs is limited. The gth was reduced from 1450 to 1280 cm−1 when the tp was reduced from 60 to 20 nm, which corresponds to a threshold modal gain (Γgth) of 29 cm−1. We evaluated the contribution of radiation loss by assuming all αi to be 0 in Table I. The outcome of radiation loss is 24.3 cm−1, while the gap of 4.7 cm−1 is attributed to internal absorption loss.

FIG. 6.

Dependence of (a) Γ, (b) Q-actor, and (c) gth on tp for p-PCSELs and n-PCSELs under the same tn + tp = 120 nm and th = 300 nm.

FIG. 6.

Dependence of (a) Γ, (b) Q-actor, and (c) gth on tp for p-PCSELs and n-PCSELs under the same tn + tp = 120 nm and th = 300 nm.

Close modal

In conclusion, we revealed that the optimal SCH structure for PCSELs is not dependent only on the total waveguide thickness. Suppressing the coupling between the SCH mode and the parasitic leaky mode is especially critical in the PCSEL design, and the optimized structure differs according to the position of the air holes. Coupling to the parasitic leaky mode could be either suppressed by a relatively thick waveguide layer or suppressed by relatively high air holes. Considering the strain management of InGaN epitaxial growth and the challenges in forming high aspect ratio air holes, the n-PCSEL structure shall be the more viable design for a low-threshold PCSEL. A similar methodology could also be applied to other III-nitride-based PCSELs from UV to green spectral regions, paving the way for future applications that require a more compact, low divergence, high-power density, and still an energy-efficient light engine.

This work was financially supported by the Ministry of Science and Technology (MOST) of Taiwan under Contract No. MOST 112-2628-E-A49-024. This work was also supported by the Higher Education Sprout Project of the National Yang Ming Chiao Tung University and Ministry of Education (MOE), Taiwan.

The authors have no conflicts to disclose.

Wen-Hsuan Hsieh: Formal analysis (lead); Investigation (lead); Software (lead). Duan-Hsin Huang: Investigation (supporting). Tien-Chiu Chen: Investigation (supporting). Po-Yang Chang: Software (supporting). Tien-Chang Lu: Supervision (equal). Chia-Yen Huang: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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