In this section, we proposed a crack-free AlN/GaN DBR structure could be fabricated with an asymmetric DBR structure by MOCVD system. The accumulation of strain energy during grown AlN/GaN DBR structure could be controlled by controlling the thickness of AlN and GaN layers in DBR structure. By carefully selecting the thickness ratio between AlN and GaN layers to match the design center wavelength with 430nm, the high reflectivity of 96% was obtained for an asymmetric DBR with only 20 AlN/GaN pairs. No cracks were observed and the stopband width for the reflectivity spectrum was 27 nm at center wavelength around 429 nm.
The GaN/AlN DBRs were grown on C-face (0001) 2-inch diameter sapphire
substrates by the EMCORE D-75 MOCVD system. Trimthylgallium (TMGa) and trimthylaluminum (TMAl) were used as Ga and Al sources, respectively, and ammonia (NH3) was used as N source. A 1 µm-thick GaN buffer layer was grown on the sapphire substrate, and then a 20-pair AlN/GaN DBR structure was grown at 1090oC under the fixed chamber pressure of 100 Torr. Three DBR samples have been grown with different thickness ratio of AlN and GaN layers. Sample A was a stander quarterwave stacks structure and used to determine the growth times, tA, and tG, of quarterwave thickness of AlN and GaN layer, respectively. The in-situ reflectance trace measurement for determining the growth time of AlN and GaN quarterwave stack is shown in Figure 3-13.
The other samples, sample B, and sample C were composed with (0.8 tA, 1.2 tG), and (1.2 tA, 0.8 tG), respectively. Figure 3-14 are the schematic of these three structures. In order to calculate the peak reflectance of asymmetric DBR structure composing of non-quarterwave stacks, the transmission matrix method was used to model the reflectance spectrum. The cross-section image was measured by high-resolution scanning electron microscopy. The surfaces of these samples were characterized by optical microscopy. Measurements on the reciprocal space maps (RSMs) of x-ray diffraction intensity were performed on the Philips X’Pert material research diffraction system
around an asymmetrical GaN (101−5) Bragg peak And the reflectivity spectrum of the AlN/GaN DBR structure was measured by the n&k ultraviolet–visible spectrometer
with normal incidence at room temperature.
In these three AlN/GaN DBR structures, which composed of a period heterostructure, strain relief mechanisms are more complex since one has to consider both the strain in each layer and the strain in the whole DBR structure. However the thicknesses of these individual layers in DBR structure are larger than the crictical thickness, AlN/GaN DBR structure was not like a coherent superlattices structure, and these individual layers would relieve strain and return their in-plane lattices constant to the unstrained state.
Considering the accumulative stress σa during the growth of AlN/GaN DBR structure can be written as individual in-plane stress in AlN and GaN layers, respectively, i and j are instead of AlN or GaN, ε is the in-plane isotropic strain, γ describes the relative extent of the biaxial strain [23], c are the stiffness constants, d is the film thickness, and a and a0 are the measured lattice parameters and the extrapolated lattice parameters for the fully relaxed case, respectively. From formula (1) and (2), the value of σa can be controlled by
)
modified the thicknesses of AlN and GaN layers in DBR structure.
The influences of varying the thickness ratio between AlN and GaN layers in DBR structure have been calculated. Figure 3-15 is the calculation result of the accumulative stress σa and the peak reflectance of 20-pair AlN/GaN DBR structure under different optical length parameter H, which was defined as:
(3-15) the material parameters used for calculation for AlN and GaN are listed in Table [3, 24].
In Figure 3-15, we supposed the strained-layers in DBR structure were unrelaxed (γ =1),
and the center wavelength of DBR structure was 430nm. The calculation result indicated that σa= 0 at H = 0.43, implying that the asymmetric AlN/GaN DBR structure with thicker optical length dGaNnGaN might compensate the tensile stress by the compressive stress. From the calculation, the accumulative stress σa for sample A, B, and C were
-13.0 GPa, 7.3 GPa, and -29.4 GPa. Sample A, a general quarterwave-stack DBR structure, exhibited a negative σa value because of the AlN thickness being larger than
the GaN thickness in one pair DBR structure. And among these three samples, sample B is the only structure with a positive σa value indicated that a compressive stress could be accumulated in one pair DBR structure. On the other hand, the calculation result of peak reflectance for 20-pair AlN/GaN DBR structure showed that the quarterwave-stack DBR structure (H = 0.5) has the highest reflectance and the reflectance decreased as the
AlN
optical path parameter H deviated from 0.5. However, the peak reflectance was calculated to be higher than 0.99 when 0.35<H<0.65. As a result, the calculated peak reflectance of 20-pairs AlN/GaN DBR structure for sample B could still be kept as high as 0.99.
The micro-photograph images of the grown AlN/GaN DBR structures were observed by the optical microscope and shown in Figure 3-16. Over the whole 2-inch wafer, a crack-free surface was observed on sample surface of sample B. On the other hand, a parallel-crack pattern and a network-crack pattern were observed on sample surface of sample A, and sample C, respectively. The average crack density determined by the micro-photograph images for sample A, B, and C were 15.6/mm, 0/mm, and 26.7/mm. It demonstrated that the generation of crack could be eliminated by controlling the thicknesses of AlN and GaN layers during the growth of AlN/GaN DBR structure, since the crack generation was due to the accumulation of tensile stress in the multiple layer structures.
In order to determine the strain in the DBRs, the XRD measurement on reciprocal space maps (RSM) around the asymmetrical (1015) Bragg peak of the GaN substrate was proceeded. Figure 3-17 (a), (b), and (c) shows the (1015) RSMs of sample A, B, and C, respectively. The lattice parameter c along the growth direction and lattice parameter a along in-plane were represented by the perpendicular axis and the parallel axis, respectively. Both axes were inversely proportional to each lattice constant. The
diffraction pattern around spots labeled A and C are due to the AlN and GaN layers, respectively, and the diffraction pattern around spots labeled B is considered as zero order peak of DBR structure. It can be seen that the location of the diffraction pattern B was shifted to GaN diffraction pattern as the thickness of AlN layers decreasing in DBR structure. Compare with the labeled C of RSM patterns, sample A and B are shown slightly strained GaN embedded between the AlN layers, but sample C is not shown strain within GaN layers. Furthermore, the in-plane strainsεxxin AlN layers can be obtained from = epi −1
x AlN x
xx q
ε q , where the qxepiand qxAlN are the x positions of the actual
epitaxy AlN film and unstrained AlN, respectively. The biaxial tensile strain in AlN layer in sample A, B and C were calculated to be 0.00722, 0.00902, and 0.00521, respectively.
These results indicate that the AlN layers are under tensile strain and the tensile strain is partially relaxed because the diffraction peaks don’t align in a vertical straight line.
However, the degree of relaxation decreases as the thickness of AlN layer in DBR structure decreasing.
Indeed, the relaxation of strain energy by generating cracks on sample surface and the relative strain parameter γcrack can be calculated from the density of generated cracks on the sample surface [23]. The calculation results of γcrack for sample A, B, and C were 0.62, 1 (crack-free), and 0.49, respectively. Beside, the relative strain parameters γ determined by the results of x-ray diffraction patterns on the RSMs were 0.36, 0.56, and 0.26 for
sample A, B, and C, respectively. Figure 3-18 shows the strain parameters versus optical length parameter H for sample A, B, and C. The difference between γcrack and γ indicated
that there are other mechanisms, such as misfit dislocation and V-trench, to relax the strain energy of AlN/GaN multi-layer structure [24]. The decreasing trends in γcrack versus H indicated that increasing the thickness of AlN layers in AlN/GaN DBR structure could easily lead to strain energy relaxation by generating cracks on the sample surface.
The reflectivity spectra of these DBRs were measured by the n&k ultraviolet-visible spectrometer with a normal incidence measurement setup. The normalized reflectance spectra of AlN/GaN DBR structures for samples of A, B, and C were shown in Figire 3-19. The stopband center of reflectance spectrum of sample A composed of quarterwave stacks DBR structure was 431 nm with a peak reflectance of 96.0% and the stopband width of 27 nm. Sample B has the similar reflectivity peak value of about 96% around 429 nm and the stopband width of 27 nm for the asymmetry AlN/GaN DBR structure.
However, the stopband center of reflectance spectrum of sample C is 436 nm with a lower peak reflectance of 90.0% and a smaller stopband width of 20 nm. It may be indicated that the generation of surface cracks due to the strain energy relaxation could lead to increasing fluctuation of the growth rate resulting in the red-shifted of stopband centers [25] and degradation of the peak reflectance and stopband width [3, 26].
In conclusion, the crack-free AlN/GaN DBR structures on (0001) sapphire were
grown by MOCVD. The peak reflectivity of a 20-pair asymmetric AlN/GaN DBR structure was about 96% with a stopband width of 27 nm around the center wavelength of 429 nm. By reducing the ratio of AlN and GaN layer thickness, the density of surface cracks per unit area could be reduced. By this approach, the realization of high quality III-nitride DBRs shall pave the way for development of nitride-based high-Q microcavity and blue VCSELs.
References
[1] Grant R. Fowles, “Introduction to Modern Optics”, Chapter 4, 1975.
[2] T. Honda, A. Katsube, T. Sakaguchi, F. Koyama, K. Iga, Jpn. J. Appl. Phys. Pt. 1 34, 3527, 1995.
[3] H.M. Ng, T.D. Moustakas, S.N.G. Chu, Appl. Phys. Lett. 76, 281, 2000.
[4] R. Singh, D. Doppalapudi, T.D. Moustakas, L.T. Romano, Appl. Phys. Lett. 70, 1089, 1997.
[5] D. Doppalapudi, S.N. Basu, T.D. Moustakas, J. Appl. Phys. 85, 883, 1999.
[6] H.M. Ng, T.D. Moustakas, S.N.G. Chu, Appl. Phys. Lett. 76, 2818, 2000.
[7] D.D. Koleske, A.E. Wickenden, R.L. Henry, J.C. Culbertson, M.E. Twigg, J. Crystal Growth 223, 466, 2001.
[8] S. Yamaguchi, M. Kosaki, Y. Watanabe, Y. Yukawa, S. Nitta, H. Amano, I. Akasaki, Appl.
Phys. Lett. 79, 3062, 2001.
[9] R. Langer, A. Barski, J. Simon, N.T. Pelekanos, O. Konovalov, R. Andre, Le Si Dang, Appl. Phys. Lett. 74, 3610, 1999.
[10] S. Fernandez, F.B. Naranjo, F. Calle, M.A. Sanchez-Garcia, E. Calleja, P. Vennegues, A.
Trampert, K.H. Ploog, Appl. Phys. Lett. 79, 2136, 2001.
[11] F. Natali, D. Byrne, A. Dussaigne, N. Grandjean, J. Massies, B. Damilano, Appl. Phys.
Lett. 82, 499, 2003.
[12] T. Someya, Y. Arakawa, Appl. Phys. Lett. 73, 3653, 1998.
[13] K.E. Waldrip, J. Han, J.J. Figiel, H. Zhou, E. Makarona, A.V. Nurmikko, Appl. Phys. Lett.
78, 3205, 2001.
[14] H.P.D. Schenk, P. de Mierry, P. Vennegues, O. Tottereau, M. Laugt, M. Vaille, E. Feltin, B. Beaumont, P. Gibart, S. Fernandez, F. Calle, Appl. Phys. Lett. 80, 174, 2002.
[15] N. Nakada, H. Ishikawa, T. Egawa, and T. Jimbo, Jpn. J. Appl. Phys., Part 2 42, L144,
2003.
[16]J. P. Zhang, H. M. Wang, M. E. Gaevski, C. Q. Chen, Q. Fareed, J. W. Yang, G. Simin, and M. Asif Khan, Appl. Phys. Lett. 80, 3542, 2002.
[17]E. Feltin, B. Beaumont, M. Laugt, P. Vennegues, H. Lahreche, M. Leroux, and P. Gibart, Appl. Phys. Lett. 79, 3230, 2001.
[18]M. Kurimoto, T. Nakada, Y. Ishihara, M. Shibata, T. Honda, and H. Kawanishi, Jpn. J.
Appl. Phys., Part 2 38, L552, 1999.
[19]Y. Ishihara, J. Yamamoto, M. Kurimoto, T. Takano, T. Honda, and H. Kawanishi, Jpn. J.
Appl. Phys., Part 2 38, L1296, 1999.
[20] D.D. Koleske, A.E. Wickenden, R.L. Henry, J.C. Culbertson, M.E. Twigg, J. Crystal Growth 223, 466, 2001.
[21] D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O.
Ambacher, M. Stutzmann, J. Appl. Phys. 82, 5090, 1997.
[22] G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, T. Jimbo, Appl.
Phys. Lett. 70, 3209, 1997.
[23] S. Einfeldt, V. Kirchner, H. Heinke, M. Dießelberg, S. Figge, K. Vogeler, and D. Hommel.
J. Appl. Phys. 88, 7029, 2000.
[24] P. Vennéguès, Z. Bougrioua, J. M. Bethoux, M. Azize, and O. Tottereau. J. Appl. Phys. 97, 024912, 2005.
[25] J.-M. Wagner and F. Bechstedt. Phy. Rev. B. 66, 125202, 2002.
[26] N. Naoyuki, I. Hiroyasu, E. Takashi and J. Takashi, Jpn. J. Appl. Phys. 42 (2003) L144.
Figure 3-1 The schematic diagram of normal incidence on a single dielectric
Table 3-1 The boundary conditions of electric and magnetic fields at each interface
First Interface Second Interface Electric:E0 +E0' =E1 +E1' E1eikt +E1'e−ikt =ET
Magnetic: H0 −H0' =H1 −H1' H1eikt −H1'e−ikt =HT or n0E0 −n0E0' =n1E1−n1E1' n1E1eikt −n1E1'e−ikt =nTET
Figure 3-2 The simulation results for DBR structures with 5, 10, 20, and 30 pairs. The refraction indices of nH and nL are set as 2.4, and 2.1, respectively.
350 400 450 500 550
0.0
350 400 450 500 550
0.0
350 400 450 500 550
0.0
350 400 450 500 550
0.0
Figure 3-3 The peak reflectance of DBR structures with different pair number.
0 5 10 15 20 25 30
0.0 0.2 0.4 0.6 0.8 1.0
Reflectance
Pairs
Figure 3-4 The simulation results for 20-pair DBR structures with ∆n=0.2, 0.3, 0.4, and 0.5, respectively.
350 400 450 500 550
0.0 0.2 0.4 0.6 0.8 1.0
Reflectance
Wavelength(nm)
∆n=0.2
∆n=0.3
∆n=0.4
∆n=0.5
Table 3-2 The arrangement of simulation result of DBR structure with different index contrast.
15-pair DBR Structure 99% DBR Structure
Δn Peak Reflectance (%)
StopBand Width (nm)
Needed Pairs
StopBand Width (nm)
0.2 91.3 24 38 25
0.3 97.8 38 25 41
0.4 99.5 55 18 56
0.5 99.9 72 14 73
Figure 3-5 The simulation result of asymmetric DBR structure.
400 425 450 475 500
0.0