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Abstract
We report continuous wave operation of electrically injected InGaN laser diodes using nano-porous GaN n-side cladding with 33% porosity. At 454 nm emission wavelength, the pulsed injection slope efficiency is 0.24 W/A with a high loss of 82 cm-1. The considerable 60 cm-1 of excess loss of the nano-porous clad lasers is attributed to scattering at pores in unintentionally 3% porosified layers, supported by numerical modeling. Simulations comparing porous GaN cladding to AlInN cladding for lasers operating at 589 nm indicate that the porous cladding provides similar internal loss and lower thermal impedance.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nano-porous GaN has seen increasing research interest for its large refractive index contrast with bulk GaN while remaining lattice matched. This is advantageous for high reflectivity distributed Bragg reflectors or cladding layers in GaN based lasers, and porous GaN has been demonstrated in blue-emitting vertical cavity surface emitting lasers [1,2] and edge emitting laser diodes (EELDs) [3–6] in this capacity.
The potential benefits of NP GaN cladding are greater at longer wavelength emission. There is a specific need for diode lasers with 589 nm emission targeting a sodium atom transition, useful for astronomical observations [7] and as part of laser cooling systems for cold molecular physics research and atomic clocks [8]. InGaN radiative efficiency sharply declines at longer wavelengths [9], making high modal confinement over the active region critical to reach threshold. It is a significant problem that the index contrast between (Al,Ga,In)N core and cladding layers also decreases as the bandgap energy drops. The longest wavelength GaN based edge emitting lasers use a combination of InGaN waveguides and AlGaN or InAlGaN cladding for modal confinement and have demonstrated lasing up to 536 nm [10]. For even longer wavelength lasers, the thickness of AlGaN cladding needed for adequate mode confinement is beyond the critical thickness for crack or defect formation. Only InAlN alloys provide high enough index contrast with minimal added strain, but are challenging to grow, requiring narrow windows for temperature, gas flow, and growth rate [11]. NP GaN cladding provides an alternative to InAlN by providing the requisite large refractive index contrast without additional strain.
The electrochemical etch used to form NP 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 [12]. NP GaN also suffers from lower electrical and thermal conductivity compared to bulk GaN, both barriers to continuous wave (CW) operation. For these reasons, we first demonstrate NP GaN clad EELDs operating at 450 nm, where the gain is high. We achieve CW operation, but with very poor differential efficiency. Examination of the LDs reveal inadvertent etching of an n-GaN waveguide (WG) core layer, and numerical analysis confirms that scattering in that layer can account for the low efficiency.
2. Experimental
The epitaxial structure was grown using atmospheric pressure metalorganic chemical vapor deposition (MOCVD) on a $(20\bar{2}\bar{1})$oriented bulk GaN substrate as displayed in Fig. 1(a). A GaN buffer of 400 nm of unintentionally doped (UID) GaN and 400 nm of 2×1018 cm-3 Si-doped n-GaN was grown at 1180 °C. Then, 180 nm of heavily Si-doped n-GaN (3×1019 cm-3) was grown, intended to serve as the n-side cladding after later porosification. This was followed by 240 nm of lightly Si-doped n-GaN and 100 nm of n-In0.01Ga0.99N, both at 2×1018 cm-3 and 1000 °C, before 35 nm of UID GaN and a quantum well (QW) active region with 2 periods of 3 nm In0.18Ga0.82N QWs and 7 nm GaN barrier layers grown at 863 °C. After ending on a barrier, a 20 nm p-Al0.28Ga0.72N electron blocking layer (EBL) was grown at 1000 °C doped with 3×1019 cm-3 Mg, and 1000 °C p-GaN with 2×1018 cm-3 for 200 nm and 1×1020 cm-3 for 20 nm. Photolithography was then used to pattern a 200 nm SiO2 hardmask, where a 3 µm deep trench was etched with Cl2 reactive ion etching (RIE), parallel to the projection of the c-axis and the direction of the eventual laser ridge. An indium contact was soldered to a corner, whereupon the sample was suspended in 0.6 M oxalic acid with conductive tweezers and electrochemically etched maintaining 5 V of applied voltage for 7 hrs.
Samples were subsequently fabricated into ridge lasers with indium tin oxide (ITO) p-contacts and chemically assisted ion beam etched (CAIBE) facets, as reported in [5]. Measurements were taken using 500 ns pulsed electrical injection with 0.5% duty cycle before the backside was polished to 150 µm, a cathode contact was deposited, and the samples soldered to a thick copper block heat sink for CW testing.
3. Discussion of results
3.1 LJV characteristics
The nano-porous clad (NPC) devices were designed with a single, highly doped porous layer for n-side cladding. Figure 2 displays an SEM image of the facet, revealing the low doped layers were also slightly porosified. The target cladding layer is 33% porous, while the unintentionally porosified layers are 3%. The interface between substrate and MOCVD grown material was also etched. Both c+ and c- facets of individual lasers inspected by SEM had similar porosities, which is assumed to be uniform across the length of the ridge. From the measured layer thicknesses by SEM and estimated porosity of the intentional and unintentional cladding layers, the NPC sample was calculated to have a 1.8% optical mode confinement over the quantum wells, determined using the commercial MODE software [13] and presented in Fig. 1(b). Note that the p-GaN waveguide layer was made unusually thin in this laser and that ITO cladding was used instead of p-AlGaN. This has been shown to reduce the voltage and optical loss and to limit the growth time at high temperature after the InGaN quantum wells have been grown [14,15]. In the absence of a high index contrast cladding layer below the wells the optical mode would be pushed deep into the n-side, reducing the mode overlap with the active region and increasing absorption loss in the n-GaN. It is for this reason that we are exploring NP-GaN as a lower cladding layer. Close examination of the mode profile in Fig. 1(b) shows that the epitaxial design was not quite right and that the center of the optical mode still falls below the quantum wells. This may partially explain the high threshold current observed and can be easily corrected.
Fig. 2. Scanning electron micrograph image a.) of CAIBE facet, b.) segmented to extract porosity in layer of interest,and c.) pore distribution above target layer
The emission spectra and light - current density - voltage (LJV) characteristics of a representative 1200 µm × 8 µm ridge are shown in Fig. 3. Under pulsed operation, threshold current density is 4 kA/cm2 at a peak wavelength of 454 nm. The impact of the high scattering loss may be seen in the reduction of photon lifetime calculated at transparency, from 3 ps if the internal loss was a typical 20 cm-1 to just 1 ps with the measured 82 cm-1 of internal loss. The β-factor was calculated to be 9.4 × 10−5 from equation A4.10 in [15]. Devices held above the surface of the acid during the electrochemical etch were not porosified and predictably did not reach threshold.
Fig. 3. a) Emission spectra and linewidth at varied current densities under pulsed electrical injection, taken with a spectrometer-limited resolution of 2nm and b) CW electrical injection of a 1200 µm × 8 µm device. LJV plots are measured from c) pulsed and d) CW electrical injection of device with same dimensions. Light collected using segmented contacts was measured to extract e) gain curves at and f) absorption curves at varying current density under pulsed operation.
The n-side metal contact was deposited on the backside of the substrate, and the electrical current path is presumed to be through the unetched matrix in the porous layer. The electrical resistance of the NPC lasers is not significantly higher than previously reported lasers [14], suggesting the electrical conductivity of the cladding is not compromised at this porosity. Assuming the bulk n-GaN resistivity is 1×10−3 Ω-cm, a 30% porous layer would be 1.3×10−3 Ω-cm neglecting carrier scattering, and likely less than 1×10−2 Ω-cm with scattering. The resulting resistance across only 180 nm would only be about 2 mΩ, negligible compared to the rest of the structure.
Under pulsed operation, the slope efficiency is very low at 0.24 W/A. Previously reported lasers from this group using traditional InGaN waveguides have been as high as 1.4 W/A [14]. The injection efficiency and internal loss were determined by plotting the measured inverse differential efficiencies against varied cavity lengths, as outlined in Coldren [16]. Assuming a calculated mirror loss αm = 14.3 cm-1 for a CAIBE facet, we find an injection efficiency ηi = 0.6, but high internal loss αi = 82 cm-1. We compared this to gain and loss measurements using the method of segmented contacts seen in GaN laser literature [17]. Two 300 µm electrically isolated p-contacts were deposited on a single ridge, separated by a 3 µm gap, and driven by separate, synchronized electrical pulses. The front facet was etched at an angle to suppress lasing, and the back facet was several hundred microns away from the rear edge of the rear contact, to suppress any reflection from the rear facet. Although multiple spatial modes can propagate in the wide ridge, care was taken to collect only light propagating in the waveguide using small numerical aperture lenses and a single mode fiber to filter spontaneous emission and scattered light. Analysis of the spectra taken with the front, back, or both contacts driven yielded the results shown in Fig. 3(b). The absorption αi = 65 cm-1 was in moderate agreement with our previous estimate. We attribute the high loss due to optical scattering at pores in the inadvertently porosified waveguide layer. The optical mode is calculated to have a 30% overlap with the low porosity layer above the cladding, and therefore any scattering in this layer has a tremendous effect on the overall internal loss, discussed in detail below.
Although the NPC devices reached threshold under CW operation, the threshold current density was much higher than during pulsed testing at 5.5 kA/cm2 with an even lower efficiency of 0.06 W/A, and power rolling over quickly. This is due to low thermal conductivity of the porous layer. Methods to improve heat dissipation in a porous cladding device are currently under investigation.
The differential modal gain was found to be 4.5 cm/kA, low compared to previously reported lasers [14]. In consideration of the measured injection efficiency and calculated optical confinement factor, the only self-consistent value for material gain was 600 cm-1 at a current density of 4 kA/cm2, also low compared to previous results. A conventionally clad laser that was grown and fabricated in the same time frame also performed poorly, perhaps indicative of crystal growth problems, but not conclusive.
The complex morphology of the nano-pores does not fit the assumptions upon which Rayleigh, Tyndall or Mie scattering approaches are based [2,4,12]. Instead, we used Lumerical FDTD software [18] to estimate the scattering from single cylindrical pores perpendicular to the optical field as a function of pore size and location within the optical field. A refractive index map of the simulated structure is shown in Fig. 4, reproducing the experimental structure. An exception was made to reduce the computational complexity by combining the quantum wells and barriers into a single active region with a thickness-weighted average refractive index of 2.48. This was justified because the optical field is nearly constant across this 55 nm thick region. The simulated structure was also truncated in the NP GaN cladding layer since the optical mode does not penetrate past this low-index layer. The effective refractive index of the 30% porous GaN cladding layer was determined using the volume average theory [12]. The refractive index of the pore was 1.0, corresponding to an air-filled void. The simulation length along the direction of propagation was 4 µm. The simulation time was 1000 fs with a 0.01 fs time step. An automatically generated conformal mesh was used, with a minimum mesh spacing of 5 nm in the structure. An auxiliary fine mesh covering the pore was added, sized to ensure at least two mesh lines in each direction across the pore. Perfectly matched layer (PML) boundary conditions were used at all boundaries, and symmetry was only invoked across the lateral dimension. The fundamental optical mode was calculated as previously described and used as the source for the FDTD simulation. To find the optical transmission past a pore, the power integrated across the entire waveguide was calculated just before the pore and again at 3 µm past the pore, just before the end of the simulation length. The transmission is the ratio of these two results and is shown in Fig. 5 for various pore sizes and locations in the optical field.
Fig. 5. Modeled transmission around single pores in waveguide layer at specified depth and varying pore sizes. The insets show perturbation to the optical mode by pores of various radii. Only the largest pores significantly perturb the mode. The simulation includes no intentional loss other than the pore scattering. The convergence to T=0.9985 instead of 1.0 persists at pore radii of 0.1 nm or in the absence of any pore, and may be due to mode mismatch arising from an inexact calculation of the input eigenmode.
Results shown in Fig. 5 indicate that, as expected, the scattering is dominated by larger pores higher in the waveguide layer where the optical field is strongest. A histogram of pore sizes was obtained by image analysis of the SEM cross section shown in Fig. 2. Relatively few pores 20 nm in radius are seen in the waveguide layer, so scattering from these pores might be treated as independent. The transmission past a collection of isolated single pores may be converted to a distributed loss by αsc=(1/L)ln(1/T), where L is the length over which the pores are distributed. The result is that just a few of the larger pores per micron of waveguide length, near the middle of the waveguide, is enough to account for the measured 82 cm-1 loss, 20 cm-1 of which may be normal internal loss. This is well within the statistical distribution shown in the histogram. We point out that scattering from the highly porous cladding layer is low because the optical field overlaps only 0.13% with the cladding.
We have noted that the pore morphology does not meet the assumptions for Rayleigh scattering. However, the numerical results confirm that the largest contribution to the scattering is from the largest pores. We believe that the large voids seen in Fig. 2 are from the intersections of narrower branching pores. The two-dimensional spacing of these larger voids averages just over 100 nm; if we assume that this spacing prevails along the third dimension the corresponding void density is about 1015/cm3. If we count only pores of radius 10 nm or larger in the histogram of Fig. 2, the median void radius is 13 nm, small enough that Rayleigh scattering might be applicable. Scattering by voids in silicon has been considered previously [19], with the analytical result that the scattering loss αsc is given by
The excess loss must be reduced by improving etch selectivity, which has been an ongoing problem for this group [5]. For higher etch selectivity, we must increase the conductivity of the target layer relative to other layers. The ideal cladding layer is highly porous for index contrast with very small pores to minimize scattering loss. This can be difficult to achieve because increasing the silicon doping in the target layer causes roughness and defect formation during epitaxial growth [20]. It is possible the target layer can be doped more heavily while maintaining good morphology with flow modulation epitaxy, using alternate growth planes [1], or by using alternative dopants such as germanium [2,18]. A more straightforward solution is rather to decrease the doping in the secondary n-type layer. Reducing doping of this 400 nm thick layer by an order of magnitude to [Si] = 2×1017 cm-3 will prevent porosification [12]. Assuming the Si donors are fully activated, the electron mobility approximately doubles from 100 cm2/V-s to 200 cm2/V-s [21] at the lower doping level. This calculates to 5 times higher resistance in the layer, and an insignificant 0.02 V penalty at 4 kA/cm2 in a 1200 µm × 8 µm ridge.
3.2 Porous vs InAlN cladding at longer wavelengths
Though NP GaN cladding has little advantage for shorter wavelength lasers such as blue, we have included new laser designs to show the potential for porous GaN to improve longer wavelengths. Lasers emitting at 589 nm peak wavelength are shown in Fig. 6 comparing porous GaN and lattice-matched InAlN cladding. Beginning with the basic blue structure from Fig. 1, the InGaN waveguide was removed and replaced with lower InAlN cladding or porous cladding. To compensate for the expected drop in material gain at 589 nm emission, the number of quantum wells was increased from two to five in this simulation, with increased indium composition. The mode profiles in Fig. 6(c) and (d) were calculated with MODE [13]. Using 100 nm of 35% porous material, and assuming a perfectly selective porosification, we reach 7% optical mode confinement. At 589 nm, the index contrast from 35% porous GaN to GaN is ΔnNP GaN-GaN = 0.3, whereas InAlN is only a third of that at ΔnInAlN-GaN = 0.1 [11]. This means over 200 nm In0.18Al0.72N cladding is needed to reach the same level of optical confinement. The mode penetrates deeper into the InAlN cladding layer than the equivalent porous layer due to lower index contrast with the core, increasing the InAlN cladding layer's contribution to the internal loss. At this long wavelength, the mode penetration into the NP GaN cladding is 5%, compared to only 0.13% at 450 nm. This mode overlap is large enough to raise concerns about excess loss from scattering, although not at the level discussed above, and perhaps ameliorated by the strong inverse dependence of scattering on wavelength. We expect that the modal loss will be similar with either InAlN or NP GaN cladding.
Fig. 6. MODE yellow laser designs with a.) InAlN cladding indices, b.) porous cladding indices, c.) InAlN cladding mode, and d.) porous cladding mode
The reduction in thermal conductivity from both porosified GaN and InAlN compromise the CW performance. Comparisons have been made between porous GaN and InAlN by several groups [22,23]. The thermal conductivities are nearly equivalent at 7 W/m-K, so we may expect to see a temperature rise in the double thickness InAlN cladding hastening thermal rollover under CW electrical injection. For a 1200 µm × 8 µm stripe heat source, thermal impedance of the InAlN cladding would double to 3 K/W from only 1.5 K/W for the NPC. Assuming a simple model for single dimensional heat flow from the active region and our measured Jth = 5.5 kA/cm2 and Vth = 8 V results in a 6 °C higher operating temperature at threshold for the InAlN based cladding.
We point out in our case that the porous layer did not fully undercut the sample, and there are likely conduction paths around the porous areas in many of the measured devices. Heat dissipation may be improved by controlling the lateral porosification depth. In this way, heat can conduct around the porous layer, similar to what is seen in thermal flow of GaN VCSELs between low conductivity dielectric DBRs [23,24].
4. Conclusions
CW operation of GaN-based lasers with nano-porous GaN lower cladding layers has been demonstrated. Excessive scattering loss in an unintentionally porosified waveguide layer led to poor differential efficiency, as determined from LJV data, segmented contact measurements, and numerical analysis of scattering from model pores. This excess loss can be overcome by improved fabrication methods. The benefits of NP GaN become more important at longer wavelengths, and analysis of lasers designed for operation at 589 nm shows that NP GaN cladding is a viable alternative to InAlN.
Funding
National Science Foundation; Solid State Lighting and Energy Electronics Center, University of California Santa Barbara; U.S. Department of Energy (DE-AR0000671); Defense Advanced Research Projects Agency (HR001120C0135).
Acknowledgments
This work was supported by the Solid State Lighting and Energy Electronics Center (SSLEEC) at UCSB. This material is based upon work supported by the DARPA under Subcontract No. HR001120C0135_Sub and Nexus Photonics, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. A portion of this work was done in the UCSB nanofabrication facility, part of the National Science Foundation (NSF) funded NNIN. This work made use of MRL Central Facilities supported by the MRSEC Program of NSF
Disclosures
The authors declare that there are no conflicts of interest related to this article
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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