Thermal Transport of Nanoporous Gallium Nitride for Photonic Applications

Thermal transport of nanoporous gallium nitride for photonic applications

Cite as: J. Appl. Phys. 125 , 155106 (2019); https://doi.org/10.1063/1.5083151 Submitted: 28 November 2018 . Accepted: 30 March 2019 . Published Online: 19 April 2019

Taofei Zhou , Cheng Zhang , Rami ElAfandy, Ge Yuan , Zhen Deng, Kanglin Xiong, Fang-Ming Chen, Yen- Kuang Kuo , Ke Xu , and Jung Han

J. Appl. Phys. 125 , 155106 (2019); https://doi.org/10.1063/1.5083151 125 , 155106

Thermal transport of nanoporous gallium nitride for photonic applications

Cite as: J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151

Submitted: 28 November 2018 · Accepted: 30 March 2019 · View Online Export Citation CrossMark Published Online: 19 April 2019

Taofei Zhou,1,2 Cheng Zhang,1 Rami ElAfandy,1 Ge Yuan,1 Zhen Deng,1 Kanglin Xiong,3 Fang-Ming Chen,4 Yen-Kuang Kuo,5 Ke Xu,3 and Jung Han1,a)

AFFILIATIONS

1Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA 2School of Science, Westlake University, 18 Shilongshan Road, Xihu District, Hangzhou 310064, Zhejiang Province, China 3Suzhou Institute of Nano-Technology and Nano-Bionics, CAS, Suzhou 215123, China 4Institute of Photonics, National Changhua University of Education, Changhua 500, Taiwan 5Department of Physics, National Changhua University of Education, Changhua 500, Taiwan

a)Email: [email protected]

ABSTRACT Recently, nanoporous (NP) GaN has emerged as a promising photonic material in the III-N family. Due to its attractive properties, such as its large refractive index contrast and perfect lattice matching with GaN, as well as its good electrical conductivity, photonic components and devices involving NP GaN have been successfully demonstrated. However, further development of high-performance NP GaN based electrically injected devices, such as vertical-cavity surface-emitting lasers (VCSELs) and edge emitting lasers, requires efficient heat dissipation. Therefore, in this paper, we study thermal conductivity (TC) of NP GaN, especially when incorporated into a practical distributed Bragg reflector (DBR) in a VCSEL device. Through an effective medium model, we study the theoretical effect of NP GaN morphological properties over its TC. We then experimentally measure the TC of NP GaN, with different porosities and pore wall thicknesses, which shows a high agreement with the theoretical model. We also fabricate actual NP GaN DBRs and study the large tunability and interdepen- dence among their TC (1–24 W/m K), refractive index (0.1–1.0), and electrical conductivity (100–2000 S/m) compared to other conventional DBRs. Finally, we perform a finite-element simulation of the heat dissipation within NP GaN-VCSELs, revealing their superior thermal dissipation compared to dielectric DBR based VCSELs. In this regard, this study lays the foundation for nanoscale thermal engineering of NP GaN optoelectronic and photonic devices and paves the way for their successful commercialization.

Published under license by AIP Publishing. https://doi.org/10.1063/1.5083151

I. INTRODUCTION distributed Bragg reflector (DBR) is still one of the most challeng- ing topics in III-nitride laser diodes research after two decades of III-nitride photonic devices such as edge emitting lasers 4–9 1 2,3 endeavors. It is worth noting that the AlInN ternary system (EELs), vertical-cavity surface-emitting lasers (VCSELs), and 10 other components for integrated photonic circuits are receiving latticed-matched to GaN presents an interesting solution for pho- much attention after the success in the conventional light emitting tonic designs, even though its eventual feasibility remains unclear 9 diode (LED) technology. A fundamental requirement for such pho- due to the challenges in epitaxy. tonic devices is the capability of engineering optical indices for the Recently, we reported the growth and formation of nanopo- 11,12 confinement and manipulation of photons. Such a requirement has rous (NP) GaN by an electrochemical (EC) etching process, been difficult to meet in the III-nitride material system. The through which the creation of nanoscale voids (5–50 nm in diame- ternary AlGaN system is commonly used in constructing photonic ter) in GaN dramatically reduces the index of refraction, making it structures, yet it is severely constrained as the binary end compounds a new form of epitaxial III-nitride material that is lattice-matched (GaN and AlN) have a large lattice mismatch (Δa/a ∼ 2.4%) with to GaN, highly conductive,13 and single crystalline. Photonic com- – only a modest index contrast (Δn ∼ 0.4); surely enough, AlN/GaN ponents and devices involving NP GaN, such as DBR mirrors,13 15

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-1 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

optically pumped VCSELs, and resonant-cavity LEDs, have been temperature. A positive bias was applied across the sample by a – successfully demonstrated.16 18 Furthermore, by increasing the source meter (Keithley 2400), while a Pt wire was used as a fi ff optical con nement with engineered NP GaN cladding layers, we cathode. After EC etching, the protective SiO2 was stripped o with have demonstrated through optical pumping a much reduced abuffered oxide etch (BOE). threshold in III-nitride EELs.19 For electrically injected devices, especially those operating under high current densities such as EELs and VCSELs, efficient B. Morphology and optical properties’ characterization thermal management for rapid heat dissipation is essential for high The morphology of the nanoporous samples was characterized device performance. Indeed, commercialization of GaN-VCSELs by scanning electronic microscopy (SEM, Hitachi SU-70). SEM using two dielectric DBR mirrors have been impeded by their poor images were scanned digitally to an image processing software to ∼ thermal conductivity (TC, 1 W/m K), in spite of their nearly ideal measure the porosity, pore size, and wall thickness of NP GaN. The fl 20–22 re ectance spectrum and reasonably low lasing threshold. In porosity was calculated by dividing the total area of the voids to the this regard, the purpose of this paper is to investigate the TC prop- entire area of the porous medium. The reflectance spectrum of erties of NP GaN, especially when incorporated into a practical the GaN/NP GaN DBRs was measured using a microreflectance DBR structure in a VCSEL device. First, we study the theoretical setup with a spot size of ∼20 μm, which was calibrated against a dependence of TC of a porous medium on the volumetric porosity commercial single-crystal silver mirror. The reflectance of Si was fi ff and the wall thickness using a modi ed e ective medium theory. also measured and compared with the published data, and the pre- We then prepare, based on the model predictions, NP GaN with cision was determined to be within 0.1%. different porosities and wall thicknesses, by varying the doping concentration and the anodization voltage during EC etching. We first estimate the TC of the bulk GaN film on sapphire which C. Measurement of the dislocation densities of depends on the thickness and dislocation density.23,24 Then, we unetched bulk GaN and NP GaN on sapphire measure the NP GaN samples’ TC experimentally and compare the The dislocation densities of unetched bulk GaN and NP GaN measured values with the model predictions. Having established were estimated using X-ray rocking curve measurement. (0002) and the TC of NP GaN, we fabricate NP GaN DBR mirrors and study (10–12) rocking curves were measured with Rigaku SmartLab their thermal properties. Finally, to benchmark our findings of NP X-ray Diffractometer. Full-width at half-maximum (FWHM) was GaN and to provide additional insight into heat transport, we carry extracted and used for estimation of the threading dislocation out a finite-element modeling of heat dissipation in GaN-VCSELs densities. with either dielectric DBRs or NP GaN DBRs. The result clearly indicates the advantage and promise of employing NP GaN in photonic devices to engineer the refractive index. D. Measurement of the TC of NP GaN – II. EXPERIMENTAL TC was measured using a microfabricated heater sensor pattern. A spiral metal coil with a radius of 40 μm was used as both A. Preparation of NP GaN a microheater and a resistivity-based temperature sensor.26 Before fi NP GaN was created through a conductivity selective EC metal deposition, we rst deposited a 50 nm SiO2 layer by PECVD etching process described in detail elsewhere.12,25 First, an epitaxial as an electrical insulation layer between the heating element (Ni fi structure consisting of five n+-GaN layers with different doping con- coil pattern) and the NP GaN thin lms. A spiral-coil pattern was ff centrations, separated by UID-GaN layers, was grown on a c-plane obtained through E-Beam evaporation and a lifto process of a sapphire. Afterward, standard test samples for TC measurement 50 nm-thick nickel layer. A DC current was applied via the two consist of an n+-type GaN of 500 nm in thickness to be porosified contact pads at opposite ends of the spiral-coil microheater and the according to designed parameters. Underneath the highly doped resulting resistance was sensed by a four-wire measurement after a 18 −3 stabilization time of 100 s. layers, a moderately doped n-GaN layer (ND =5×10 cm ) with a thickness of 1 μm was grown to ensure uniform distribution of the anodization bias across the entire sample during EC E. Heat dissipation simulation in VCSELs etching. Additionally, DBR samples were also prepared to examine and confirm the TC of optically engineered NP GaN A comparative study of the thermal conduction properties DBRs. The DBR samples have an epitaxial structure grown on a between NP DBR based VCSELs and dual-dielectric VCSELs was c-plane sapphire consisting of 35 pairs of alternating n+-GaN conducted through numerical modeling by the Photonic Integrated 19 −3 27 (ND =4×10 cm ) and UID-GaN layers. Circuit Simulator in 3D (PICS3D) simulation program. The After growth, the sample surface was covered with a silicon thermal modeling used basic heat generation and thermal conduc- dioxide (SiO2) layer through plasma-enhanced chemical vapor dep- tion theories that involved heat sources such as Joule/optical osition (PECVD), which was then lithographically patterned into heating, recombination heating, radiative heating, and Thomson/ – 100 μm wide stripes, separated by 10 μm openings. The sample was Peltier heating.22,28 30 Temperature profiles were numerically then dry-etched by Cl-based reactive ion etching (RIE) to create modeled and recorded as heat maps in the cross section of the two trenches and to expose the sidewalls of the highly doped n+-GaN different VCSEL structures (refer to the supplementary material for layers. EC etching was conducted in an acid electrolyte at room details).

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-2 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

III. RESULTS AND DISCUSSION A. Theoretical model of nanoporous GaN thermal conductivity The TC of porous medium strongly depends on the porosity and size of nanopores, especially when its characteristic lengths are comparable to the phonon mean free path (MFP). For a more quan- titative understanding, we used a modified effective medium model as a theoretical guideline31,32 to describe the heat transfer in porous ÀÁ1 l0 medium. The model appears as κeff ¼ κ0f (w)1þ ,where w κ D is the porosity of NP GaN, 0 is the TC of bulk GaN (130 W/m K), f(w)=(1− w)/(1 + w)istheeffective medium modified by macroscopic porosity of a composite material,33 and the parenthetical term includes the effect of phonon scattering or 34 phonon bottleneck in nanostructures. l0 is the MFP of phonons κ and D is the wall thickness (refer to the supplementary material). 0 FIG. 2. Processing phase diagram for EC etching. Two sets of samples labeled was determined to be 130 W/m K based on the thickness as solid circles of three different colors were studied for the investigation of TC − (2.5 μm) and dislocation density (5 × 108 cm 2).35 The dislocation of NP GaN. The first set of samples (blue and green series) had the same density of the GaN film was a rough estimation based on the mea- doping levels. The second set of samples (red series) was designed to follow surement of FWHM in the X-ray rocking curves, as shown in Fig. 1. the isoporosity curve near the low-porosity side of the EC etching phase diagram. As the wall thickness becomes close to the MFP of phonons, there will be a rapid decrease of TC due to phonon-nanopore scattering. On the other hand, the TC decreases as the porosity increases as a ff result of reduced e ective medium. Thus, the two most important general trend as depicted schematically by the white circles in determining parameters for TC, as predicted by the model, are the Fig. 2 is summarized as follows: both a low doping and low bias porosity and wall thickness of the NP GaN. Experimentally, it is lead to a small pore diameter. A low doping is effective in increas- worth noting that the wall thickness D is often correlated with poros- ing the wall thickness (interpore separation) based on the w w ity , and there is a general trend of increase in D with decreasing . depletion-region model.11 Based on the theoretical model, three sets of NP GaN samples were prepared with process parameters labeled as solid circles of B. Preparation and observations of NP GaN three different colors in Fig. 2. The first two set of samples (B series morphology and C series) had the same doping levels, and the third set of Figure 2 summarizes an EC etching phase diagram of GaN. samples (A series) was designed to follow the isoporosity curve The phase diagram consists of no-etching, nanoporous etching, near the low-porosity side of the EC etching phase diagram. and electropolishing regions, and provides guidelines to design the The SEM images of samples A1–A3 and C1–C3 were shown NP GaN nanostructures, which will be used to investigate the TC in Figs. 3(a)–3(c) and 3(d)–3(f), respectively. For n+-GaN at higher − of NP GaN. In traversing from the “no-etching” (lower left corner) doping levels such as 1 × 1020 cm 3 (samples B1 and B2), the pore to “electropolishing” (upper right corner) regions, there is a contin- size and porosity have been reported in our previous publications.13 uous increase of the overall porosity. The effect of doping and Statistical results of porosity (w) and average wall thickness (D) for applied bias on the pore morphology is somewhat intertwined. The all these NP GaN samples were summarized in Table I.Aswe

FIG. 1. Symmetric (0002) (a) and (10–12) (b) rocking curves of unetched bulk GaN and EC etched NP GaN (porosity ∼47%) ﬁlms on sapphire.

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-3 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

FIG. 3. Cross-sectional SEM images of samples etched at different doping levels and etching voltages. The sample numbers correspond to the annotations in Fig. 2.

could observe, the constant doping series (B and C) had similar D an 80-μm diameter, spiral Ni coil was patterned onto the but different w, while the isoporosity series (A) showed a major described 8 samples (Fig. 2) as well as a reference sample contain- change in D and a slight change in w. Based on w and D, we used ing no NP GaN (Fig. 4). In such a technique, the thermal conduc- the modified effective model to calculate TC of the NP GaN tivity of the test samples can be determined with the knowledge κ fl samples, and the results were named as NP GaN calculated and sum- of generated heat ux (Q, controlled by the microheater) and cor- marized in Table II. responding temperature increase ΔT (measured by the Ni-thermometer).26,36 The ΔT changed almost linearly with heat C. Thermal conductivity measurement of NP GaN flux within the input power range (Fig. 5). To reduce the error To directly measure the TC of NP GaN and test the model predictions, a differential temperature technique was used, where TABLE II. The measured and calculated TC (κNP GaN) data obtained at the input power of 100 mW.37 TABLE I. The extracted porosity and wall thickness data from the SEM images. Calculated TC from Measured TC from Doping Wall effective medium model microheater–sensor κ κ concentration Applied Porosity thickness NP GaN calculated NP GaN measured − Sample (cm 3) bias (V) (%) (±2) (nm) (±2) Sample (W/m K) (W/m K) A1 8 × 1019 1.25 30 5 A1 4.0 3.37 A2 2 × 1019 2.0 21 14 A2 10.1 9.45 A3 1 × 1019 3.0 10 31 A3 25.2 24 B1 1 × 1020 1.8 62 6 B1 1.7 1.27 B2 1 × 1020 2.5 74 6 B2 1.1 0.83 C1 4 × 1019 1.3 24 10 C1 7.9 7.23 C2 4 × 1019 1.5 36 8 C2 4.0 3.18 C3 4 × 1019 2.0 51 7 C3 2.6 2.24 DBR (1.3 V) 4 × 1019 1.3 24 10 DBR (1.3 V) 6.96 DBR (1.5 V) 4 × 1019 1.5 36 8 DBR (1.5 V) 3.29

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-4 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

FIG. 4. Schematics of the structures for TC measurement. (a) Cross-sectional schematics of the reference sample. (b) Cross-sectional schematics of the sample structure with NP GaN. (c) A top-view optical micrograph image of a sample with the spiral-coil patterned Ni microheater.

from the convection and radiation heat loss, a very small ΔT and sample and NP GaN sample is about 5 °C and 15 °C, respectively. heat flux in Fig. 5 were extracted from the linear regions of the In static air, the heat transfer coefficient from air convection is curves to calculate the TC. Here, we have a simple evaluation of below 20 W/m2K. As a result, the maximum convection heat loss the convection and radiation heat losses. Under the heat flux of in our samples is about 1.5 μW. The power radiated through 100 mW, the maximum temperature increase in our reference black-body radiation can also be estimated to be about 2.6 μW. Clearly, the convection and radiation heat loss are negligi- ble compared to the heat flux of 100 mW. By calculating the difference in ΔT between the reference and Δ Δ test samples ( T1 and T2), the thermal conductivity from the ff κ di erent NP GaN layers ( NP GaN measured) was successfully extracted by κ ¼ Q Δ l , where l was the thickness of NP NP GaN ΔT2ΔT1 A GaN and A was the area of the Ni pattern (see the supplementary material). The results were summarized in Table II. As presented, based on the porosity and wall thickness, the TC of NP GaN can be varied from below 1 to more than 20 W/m K. Such a strong dependence is expected when the feature size of the porous medium is comparable or less than the phonon MFP in GaN crystal.

FIG. 6. TC as a function of porosity. Blue and green circles represent the exper- FIG. 5. Temperature increases of the Ni microheater (ΔT) as a function of Joule imental results and calculation results using the experimental porosity and wall heating power at thermal equilibrium in NP GaN samples and reference struc- thickness D, respectively. Solid grey lines correspond to the calculations for dif- ture for (a) A series together with C2 in C series, (b) C series, and (c) B series. ferent wall thicknesses D, i.e., 2, 6, 10, 14, 18, 22, 26, and 30 nm, respectively.

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-5 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

structure is composed of parallel aligned nanopores thus ∼ w1/2 fi Rp D × . Hence, we simpli ed our analysis of the TC of NP GaN only using the porosity and wall thickness. A somewhat abrupt, upward transition of experimental TC values from A1 to A3 in Fig. 6 as porosity reduces can be attributed to the coupled effect of an increase in wall thickness. It is worth noting that the large tunability of TC by changing nanoporous physical parameters, especially the nanoporous wall thickness. On the one hand, a reduction in porosity leads to a mod- erate improvement in TC, as indicated as the black curve in Fig. 6, as a result of an increased effective medium. On the other hand, by widening the pore wall thickness, the TC can be sharply improved, owing to much reduced phonon interaction at the nanopores. For NP GaN layers with large wall thicknesses and small porosities, the TC is capable of reaching more than 20 W/m K, a result very encouraging for the practical usage of NP GaN in photonic devices requiring fast heat dissipation.

FIG. 7. A parameter plot for NP GaN in comparison with other materials. 2. Design of real photonic layers, using a DBR as a case study D. Discussion As previously described, a potential interesting application of NP GaN is the development of DBR mirrors for VCSELs. Given 1. Agreement between the model and measurement the stringent requirement for the DBRs, different physical proper- Comparing the measured TC using the microheater method ties need to be considered and engineered. Based on our present κ with the calculated eff using the model (blue and green circles in and previous studies, we can summarize the optical (index con- Fig. 6, respectively), we observe a good agreement between the trast),13 electrical,13,38 and thermal properties of NP GaN, juxta- experimental data and calculation results, which lends credibility to posed with data from other DBRs (AlInN/GaN, AlN/GaN, and 22,39,40 the estimated TC values for NP GaN from the model. The grey SiO2/Ta2O5) reported in the literature (Fig. 7). As observed, solid curves represent calculated TC at different wall thicknesses as the tunability of NP GaN offers the most flexible range of design. a function of porosity. It should be noted that pore size Rp, wall Particularly, in the absence of DBR mirrors with high TC for the thickness D, and porosity w have a coupling relationship, i.e., any state-of-the-art GaN-VCSELs, NP GaN/GaN DBR offers an engi- one of the three parameters can be determined by the other two neering choice with a comparable TC with AlInN/GaN DBRs, and assuming a certain void geometry. In our case, the NP GaN 10 times increased TC compared with that of dielectric DBRs.

FIG. 8. (a) Schematic structure of DBRs mirror with NP GaN layers. Cross-sectional SEM images of DBRs with NP GaN layers etched at (b) 1.3 V and (c) 1.5 V, respectively. (d) Experimentally measured reﬂectance spectra from a DBRs region. (e) The temperature increases of the Ni microheater ΔT as a function of Joule heating power at thermal equilibrium in DBRs samples and reference sample.

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-6 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

FIG. 9. Comparison in temperature proﬁles between a double-dielectric VCSEL (a) and a hybrid NP dielectric VCSEL (b) working at CW operation with an injection power of 10 mW.

To validate our study and design choices, we prepared two NP continuous wave (CW) operation of 10 mW (4 V and 2.5 mA). + ff GaN DBR structures consisting of 35 alternating n -GaN (ND = Current crowding e ect was also included in this study. The heat − 4×1019 cm 3) and UID-GaN layers, etched at 1.3 and 1.5 V. generated from the active region primarily dissipates through the Figures 8(a)–8(c) show the schematic structure and cross-sectional metal contacts and a heat sink. Figure 9 showed the temperature SEM images of GaN/NP GaN DBR mirrors etched at 1.3 and 1.5 V, profiles in the two VCSEL structures, respectively. As shown which have porosities of 24% and 36%, respectively. Reflectance of in Fig. 9, the double-dielectric VCSEL shows a heat built-up of the two samples [Fig. 8(d)] shows peak reflectance exceeding ∼100 °C (372.6 K) in the active region, indicating the difficulty in 99.8%, at a designed central wavelength of 460 nm, with a stop heat transport through the dielectric bottom DBR. In contrast, the band of more than 50 nm. Furthermore, the measured TC of the NP DBR based VCSEL shows much improved hear transfer, thanks NP GaN layers in the DBRs etched at 1.3 and 1.5 V were 6.96 and to the high lateral TC; the highest temperature in the active region 3.29 W/m K, respectively, resulting in an average TC of 12.3 and was 50 °C lower than in the double-dielectric VCSEL case. With 6.0 W/m K in the NP DBR, respectively. the advantage of improved thermal conduction properties, the NP It is worth pointing out that the measured TC for DBRs DBR based VCSELs will be able to work at much lower operation in Fig. 8 and Table II are based entirely on vertical heat flow, temperatures, which should benefit the threshold, power, and where the TC is dominated by the NP GaN layers in series efficiency of devices. with GaN layers. In actual VCSEL devices, the lateral heat flow involves summing up the thermal “conductance” of layers in parallel, which will be dominated by the GaN layers. So, the IV. SUMMARY TC of the DBR layers behaves as porouslike in the vertical direction and GaN-like in the lateral direction. Such an anisot- To summarize, in this study, we investigated the TC of NP GaN, especially when incorporated into a DBR structure for ropy in the lateral and vertical directions is advantageous for fl fast heat dissipation in the lateral direction. Here, it should be VCSELs. To clarify the respective in uence on TC, key parameters noted that since the nanopores are parallel aligned in the were varied systematically associated with NP GaN, including volumetric porosity, average pore size, and average wall thickness. A lateral direction and thus have a geometry anisotropy, there ff might also be an anisotropy in TC along the lateral and verti- theoretical e ective medium thermal conduction model has been put forward and agrees well with the direct measurement by a cal directions. The lateral TC is not studied but is expected to ff be enhanced by the continuum of pore walls along the pore spiral-coil microheater/sensor method. Considering the trade-o s in employing NP GaN as a low-index layer, parameter space and alignment direction, and thus probably exceed the TC in the fi fi vertical direction. For simplicity, we assume an isotropic TC of pathways were identi ed where the need of strong con nement NP GaN in Sec. III D 3. with a low-index layer using a high porosity and the need of good TC with a low porosity can be balanced. To benchmark our findings of NP GaN and to provide operational insight into heat 3. Numerical simulation of heat dissipation in VCSELs transport, we carried out a finite-element modeling of heat dissipa- Numerical modeling was conducted on two different VCSEL tion in GaN-VCSELs with either dielectric DBRs or NP GaN designs, a NP DBR based VCSEL and a double-dielectric VCSEL, DBRs. The result clearly indicated the advantage and promise of to compare the effect of the DBR materials on the heat dissipation employing NP GaN as a low-index layer for injected lasers includ- property. The two VCSEL structures were simulated under a ing EELs and VCSELs.

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-7 Published under license by AIP Publishing. Journal of Applied Physics ARTICLE scitation.org/journal/jap

17 SUPPLEMENTARY MATERIAL B.-C. Shieh, Y.-C. Jhang, K.-P. Huang, W.-C. Huang, J.-J. Dai, C.-F. Lai, and C.-F. Lin, Appl. Phys. Express 8, 082101 (2015). 18 See the supplementary material for the details of (a) parameter S.-M. Lee, S.-H. Gong, J.-H. Kang, M. Ebaid, S.-W. Ryu, and Y.-H. Cho, Opt. fi ff considerations in the modi ed e ective medium model, (b) deriva- Express 23, 11023 (2015). 19 tion of the equations for thermal conductivity measurement, and G. Yuan, K. Xiong, C. Zhang, Y. Li, and J. Han, ACS Photonics 3, 1604 (c) the VCSEL structure and parameter settings in the simulation (2016). 20 of heat dissipation. J. T. Leonard, D. A. Cohen, B. P. Yonkee, R. M. Farrell, T. Margalith, S. Lee, S. P. DenBaars, J. S. Speck, and S. Nakamura, Appl. Phys. Lett. 107, 011102 (2015). ACKNOWLEDGMENTS 21 S. Izumi, N. Fuutagawa, T. Hamaguchi, M. Murayama, M. Kuramoto, and This research was supported by the National Science H. Narui, Appl. Phys. Express 8, 062702 (2015). 22 Foundation (NSF) (Grant No. ECCS-1709149), and the facilities used S. Mishkat-Ul-Masabih, J. Leonard, D. Cohen, S. Nakamura, and D. Feezell, Phys. Status Solidi A 214, 1600819 (2017). were supported by YINQE and NSF MRSEC DMR (No. 1119826). 23 Q. Zheng, C. Li, A. Rai, J. H. Leach, D. A. Broido, and D. G. Cahill, Phys. Rev. Mater. 3, 014601 (2019). REFERENCES 24 R. Rounds, B. Sarkar, T. Sochacki, M. Bockowski, M. Imanishi, Y. Mori, 1 S. Nakamura, S. Pearton, and G. Fasol, The Blue Laser Diode: The Complete R. Kirste, R. Collazo, and Z. Sitar, J. Appl. Phys. 124, 105106 (2018). 25 Story (Springer Science & Business Media, 2013). J. Park, K. M. Song, S.-R. Jeon, J. H. Baek, and S.-W. Ryu, Appl. Phys. Lett. 94, 2 T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, and S.-C. Wang, Appl. Phys. Lett. 221907 (2009). 26 92, 141102 (2008). D. Zhao, X. Qian, X. Gu, S. A. Jajja, and R. Yang, J. Electron Packag. 138, 3 Y. Higuchi, K. Omae, H. Matsumura, and T. Mukai, Appl. Phys. Express 1, 040802 (2016). 27 121102 (2008). PICS3D, Photonic Integrated Circuit Simulator in 3D. Available at https:// 4 J. M. Redwing, D. A. S. Loeber, N. G. Anderson, M. A. Tischler, and crosslight.com/products/pics3d/ 28 J. S. Flynn, Appl. Phys. Lett. 69, 1 (1996). G. K. Wachutka, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 9, 5 K. E. Waldrip, J. Han, J. J. Figiel, H. Zhou, E. Makarona, and A. V. Nurmikko, 1141 (1990). 29 Appl. Phys. Lett. 78, 3205 (2001). A. H. Marshak and K. M. van Vliet, Solid State Electron. 21, 417 (1978). 6 30 R. Butté, E. Feltin, J. Dorsaz, G. Christmann, J.-F. Carlin, N. Grandjean, and L. L. Liou, J. L. Ebel, and C. I. Huang, IEEE Trans. Electron Dev. 40,35 M. Ilegems, Jpn. J. Appl. Phys. 44, 7207 (2005). (1993). 7 31 G. S. Huang, T. C. Lu, H. H. Yao, H. C. Kuo, S. C. Wang, C.-W. Lin, and J. C. M. Garnett, Proc. R. Soc. Lond. 73, 443 (1904). 32 L. Chang, Appl. Phys. Lett. 88, 061904 (2006). I. Sumirat, Y. Ando, and S. Shimamura, J. Porous Mater. 13, 439 (2006). 8 33 Z.-Y. Li, T.-C. Lu, H.-C. Kuo, S.-C. Wang, M.-H. Lo, and K. M. Lau, J. Cryst. N.-W. Park, W.-Y. Lee, T.-H. Park, D.-J. Kim, S.-H. Cho, S.-Y. Lee, and Growth 311, 3089 (2009). S.-K. Lee, J. Alloys Compd. 639, 289 (2015). 9 34 G. Cosendey, A. Castiglia, G. Rossbach, J.-F. Carlin, and N. Grandjean, Appl. G. Romano and J. C. Grossman, Phys. Rev. B 96, 115425 (2017). 35 Phys. Lett. 101, 151113 (2012). T. E. Beechem, A. E. McDonald, E. J. Fuller, A. A. Talin, C. M. Rost, 10 K. Ikeyama, Y. Kozuka, K. Matsui, S. Yoshida, T. Akagi, Y. Akatsuka, J.-P. Maria, J. T. Gaskins, P. E. Hopkins, and A. A. Allerman, J. Appl. Phys. 120, N. Koide, T. Takeuchi, S. Kamiyama, M. Iwaya, and I. Akasaki, Appl. Phys. 095104 (2016). 36 Express 9, 102101 (2016). Engineering ToolBox, (2003). Resistivity and Conductivity - Temperature 11 D. Chen, H. Xiao, and J. Han, J. Appl. Phys. 112, 064303 (2012). Coefficients for Common Materials. [online] Available at: https://www. 12 Y. Zhang, S.-W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and engineeringtoolbox.com/resistivity-conductivity-d_418.html 37 J. Han, Phys. Status Solidi B 247, 1713 (2010). J. Ma, X. Wang, B. Huang, and X. Luo, J. Appl. Phys. 114, 074311 13 C. Zhang, S. H. Park, D. Chen, D.-W. Lin, W. Xiong, H.-C. Kuo, C.-F. Lin, (2013). 38 H. Cao, and J. Han, ACS Photonics 2, 980 (2015). C. Zhang, K. Xiong, G. Yuan, and J. Han, Phys. Status Solidi A 214, 1600866 14 D. Chen and J. Han, Appl. Phys. Lett. 101, 221104 (2012). (2017). 15 39 S.-M. Lee, J.-H. Kang, J. K. Lee, and S.-W. Ryu, Electron. Mater. Lett. 12, 673 H. Tong, J. Zhang, G. Liu, J. A. Herbsommer, G. S. Huang, and N. Tansu, (2016). Appl. Phys. Lett. 97, 112105 (2010). 16 40 F.-H. Fan, Z.-Y. Syu, C.-J. Wu, Z.-J. Yang, B.-S. Huang, G.-J. Wang, Y.-S. Lin, S. R. Choi, D. Kim, S.-H. Choa, S.-H. Lee, and J.-K. Kim, Int. J. Thermophys. H. Chen, C. H. Kao, and C.-F. Lin, Sci. Rep. 7, 4968 (2017). 27, 896 (2006).

J. Appl. Phys. 125, 155106 (2019); doi: 10.1063/1.5083151 125, 155106-8 Published under license by AIP Publishing.