growth has been achieved of al 0 . 84 in 0 . 16 n / gan dbrs near lattice - matched to gan . such dbrs are optically equivalent to state - of - the art al 0 . 6 ga 0 . 4 n / gan mirrors and avoid the issues related to strain . layers were grown in an aixtron 200 / 4 rf - s metalorganic vapor phase epitaxy system , on 2 - inch c - plane sapphire substrates . the growth was initiated by a low - temperature gan nucleation layer followed by a 1 μm thick gan buffer layer . alinn was deposited between 800 ° c . and 850 ° c . and at 50 to 75 mbar pressure using n 2 carrier gas . lower growth temperatures led to lower crystalline quality as revealed by high resolution x - ray diffraction ( hrxd ) ( 0002 ) scans . higher growth temperatures resulted in decreased indium incorporation so that near - lattice matched alloys could no longer be obtained . deposition rates ranged between 0 . 6 and 0 . 2 μm / h . during the dbr runs , growth was interrupted at each interface . gan was deposited at 1050 ° c . using h2 and n2 carrier gas . no degradation of alinn could be detected on account of thermal cycling as shown in fig1 which compares ( 0002 ) hrxd rocking curves of a 0 . 5 μm al 0 . 84 in 0 . 16 n layer with that of a 20 pairs of al 0 . 84 in 0 . 16 n / gan dbr centered at 515 nm wavelength . the hrxd scans were performed without a slit on the detector ; in this case the diffracted intensity is integrated over a 5 ° detector angle , and the full widths at half maximum ( fwhm ) of the peaks are influenced by both compositions fluctuation and c - axis tilt . the dbr superlattice satellites are not resolved on the dbr sample , as their spacing is too narrow , and the x - ray scan rather reflects the quality of the bulk materials . the single - layer and the dbr sample show identical high crystalline quality , with 360 ″ fwhm for the al 0 . 84 in 0 . 16 n peak , nearly as narrow as the 340 ″ fwhm gan peak . we have evaluated the optical index contrast between alinn and gan , δn / n =( n alin − n gan )/ n gan , by recording the reflectivity of the layers in situ during the growth of a few periods of a dbr whose center wavelength matched that of the measurement wavelength . the experimental set - up consisted of a luxtron tr - 100 using a 950 nm wavelength source under normal incidence , which allows for an absolute reflectivity measurement . fig2 shows the evolution of reflectivity during a typical run ; the growth of the gan buffer layer is stopped when its maximum reflectivity is reached around 26 %, then alinn is grown during the negative slope of the reflectivity signal , followed by gan during the positive slope . if r i is chosen to denote the reflectivity value after deposition of the i th dbr period , r i increases with the number of periods starting from the very first period . this already indicates that alinn has a lower optical index than gan , otherwise reflections at the alinn / gan and gan / alinn interfaces would be in anti - phase with the gan / air and sapphire / gan reflections , leading to a decrease of r i during the first periods . as reflections at all interfaces are in phase , the well - known formulas for dbrs reflectivity can be used for calculating the optical index contrast from the period - to - period increase in reflectivity using :  δ ⁢ ⁢ n  n ⁢ ( i ) = 1 - ( 1 + r i ) ⁢ ( 1 - r i + 1 ) ( 1 - r i ) ⁢ ( 1 + r i + 1 ) ( 1 ) this relationship is valid in the absence of parasitic effects , such as absorption , appearance of cracks or development of surface roughness which decrease the reflectivity . for verification of equation ( 1 ), a plot of δn / n as a function of the number of periods is shown in the inset of fig2 . any parasitic effect will manifests itself by a decrease of δn / n . in the case of the run shown in fig2 , a marked decrease occurs at the 7 th period , and indeed , further examination of the sample revealed the presence of cracks . this sample was still quite near lattice - matched , with an estimated about 0 . 4 % compressive strain . on more mismatched samples , cracks appeared earlier , and in some cases only the first period could be taken into account for index contrast evaluation . fig3 summarizes the index contrast measured on different samples , and presents the dependence of δn / n as a function of the indium content as estimated from hrxd ( 0002 ) measurements . open symbols represent the in - situ measurements described above for δn / n at λ = 950 nm and at growth temperature . the two other data points correspond to ex - situ analysis of the blue - green dbrs tuned at 455 nm and 515 nm presented further below . it is noted that the index contrast is not much dependent on wavelength within this range . the experimental data are well fitted by a linear dependence with indium content within the 6 % to 21 % explored range , according to : δ ⁢ ⁢ n n ⁢ ( al 1 - x ⁢ in x ⁢ n / ga ⁢ n ) = - 0 . 127 + 0 . 35 ⁢ x ( 2 ) extrapolation of equation ( 2 ) to zero indium content gives a − 12 . 7 % index contrast for aln / gan , in agreement with literature values . the advantage of using near lattice matched alinn as the low - index material is evident from fig4 , where the alinn / gan index contrast is plotted as a function of lattice mismatch to gan and compared with that of the algan / gan material system . a lattice mismatch that lies within ± 0 . 5 % is sufficient to avoid relaxation in blue dbr applications . in this case the maximum index contrast achievable with algan / gan is about 3 %, while more than 8 % is obtained with alinn / gan . the gain is even more pronounced when considering laser applications where the lattice mismatch is rather limited to ± 0 . 25 %. to demonstrate the interest of the alinn / gan system . fig5 shows the reflectivity spectra of two alinn / gan dbrs having stop bands in the visible wavelength range . sample a is a 10 period dbr centered at 455 nm , sample b has 20 periods and is centered at 515 nm . growth and reflectivity data are reported in table 1 . careful examinations by phase contrast microscopy just after the growth showed that both samples were completely crack - free over the full 2 - inch area . however , some cracks — about ten — appeared after some weeks of handling under ordinary conditions without special care . the measurements were performed with a cary 500 reflectometer in double - reflection mode . the measurement data where fitted with a standard transfer matrix model to extract the index contrast values of fig4 . the 10 - periods sample shows a maximum reflectivity of 76 % with a 41 nm fwhm stopband . for the 20 - periods sample , the reflectivity reached over 90 % with a 35 nm fwhm stopband . for comparison , nakada et al ., applied physics letters vol . 79 ( 2001 ), p . 1804 have reported 70 % and 83 % reflectivity respectively for 10 and 20 periods al 0 . 6 ga 0 . 4 n / gan dbrs relaxed on gan . hall measurements showed a residual donor density of 7 · 10 17 cm − 3 in the al 0 . 84 in 0 . 16 n layer . this value represents an upper - limit estimate as a bi - dimensional electron gas may be present at the alinn / gan interface . preliminary reflectivity data also indicate the presence of an optical transition around 4 . 2 ev , in agreement with the value reported for the al 0 . 84 in 0 . 16 n bandgap measured on layers deposited by plasma source molecular beam epitaxy and sputtering . further preferred embodiments of the invention can include dopants for electrical conductivity , e . g . magnesium for p - type conductivity or silicon for n - type conductivity . deposited materials can include diluents , e . g . boron , aluminum , gallium , indium , phosphorus , arsenic and / or antimony , typically in a combined amount not exceeding 10 percent . instead of abrupt compositional changes between layers , compositional transitions can be gradual . reflector structures of the invention can be included in optoelectronic devices such as vertical surface emitting lasers , resonant - cavity diodes , light - emitting diodes . waveguide structures of the invention can further include active regions , as in laser diodes , quantum - cascade lasers and optical modulators , for example .